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\newblock Condensed version in\,: {\em 32nd Annual Symposium on Foundations of
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St. Louis,
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\newblock {Technical Report}, Department of Industrial Engineering and
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\newblock Implementation of an interior point algorithm for linear programming.
\newblock {Technical Report}, Department of Industrial Engineering and
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I.~Adler, N.~K. Karmarkar, M.~G.~C. Resende, and G.~Veiga.
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\newblock {\em ORSA Journal on Computing}, 1:84--106, 1989.

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\newblock {\em Mathematical Programming}, 44:297--335, 1989.
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
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\newblock Limiting behavior of the affine scaling continuous trajectories for
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\newblock An interior point algorithm applied to a class of convex separable
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
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\newblock Limiting behavior of the affine scaling continuous trajectories for
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\newblock {\em Mathematical Programming}, 50:29--51, 1991.

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I.~Adler and R.~D.~C. Monteiro.
\newblock A geometric view of parametric linear programming.
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\newblock A randomized scheme for speeding up algorithms for linear and convex
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\newblock On implementing interior point methods for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
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\newblock On the exact solution of a system of linear homogeneous equations via
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\newblock A short proof of {Karmarkar's} main result.
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\newblock A globally convergent interior point algorithm for general
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\newblock {Technical Report} 97--14, Department of Computing, Imperial College
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\newblock {\em Nearest point problems\,: {Theory} and algorithms}.
\newblock PhD thesis, University of Michigan, Ann Arbor, Michigan, USA, 1990.

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\newblock A {Newton} based radius reduction algorithm for nearest point
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\newblock {\em ORSA Journal on Computing}, 6:282--289, 1994.

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A.~Y. Alfakih, A.~Khandani, and H.~Wolkowicz.
\newblock An interior--point algorithm for the {Euclidean} distance matrix
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\newblock {Research Report} CORR~97--9, Department of Combinatorics and
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\newblock {\em Combinatorial optimization with interior point methods and
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\newblock PhD thesis, University of Minnesota, Minneapolis, Minnesota, USA,
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\newblock A sublinear--time randomized parallel algorithm for the maximum
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\newblock {\em Proceedings of the Second ACM--SIAM Symposium on Discrete
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\newblock Combinatorial optimization with semi--definite matrices.
\newblock In E.~Balas, G.~Cornu{\'e}jols, and R.~Kannan, editors, {\em
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\newblock Optimization over the positive semi-definite cone\,:
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\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
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\newblock Interior point methods in semidefinite programming with applications
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\newblock {\em SIAM Journal on Optimization}, 5:13--51, 1995.

\bibitem{ipm:Alizadeh9}
F.~Alizadeh, J.-P.~A. Haeberly, M.~V. Nayakkankuppam, and M.~L. Overton.
\newblock {SDPpack} user's guide, version 0.8beta.
\newblock {Technical Report} 734, Department of Computer Science, New York
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\newblock {SDPpack} user's guide, version 0.9beta.
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\bibitem{ipm:Alizadeh8}
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\newblock A new primal--dual interior--point method for semidefinite
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\newblock In J.~G. Lewis, editor, {\em Applied Linear Algebra (Proceedings of
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\bibitem{ipm:Alizadeh6}
F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
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\newblock {RUTCOR Research Report}, RUTCOR -- Rutgers Center for Operations
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F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
\newblock Primal--dual interior--point methods for semidefinite programming.
\newblock {RUTCOR Research Report}, RUTCOR -- Rutgers Center for Operations
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\newblock Also published as\,: Technical Report, Courant Institute of
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F.~Alizadeh, J.-P.~A. Haeberly, and M.~L. Overton.
\newblock Primal--dual interior--point methods for semidefinite programming\,:
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\newblock {\em SIAM Journal on Optimization}, 8:746--768, 1998.

\bibitem{ipm:Alizadeh12}
F.~Alizadeh and S.~Schmieta.
\newblock Optimization with semidefinite, quadratic and linear constraints.
\newblock {RUTCOR Research Report} RRR\,23--97, RUTCOR -- Rutgers Center for
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\newblock An application of an interior point method for problems with
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\newblock The interior point method for nondifferentiable optimization.
\newblock {\em Journal of Computer and Systems Sciences International},
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\bibitem{ipm:Altman5}
A.~Altman.
\newblock {\em QHOPDM} -- {A} higher order primal--dual method for large scale
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\newblock {\em European Journal of Operational Research}, 87:200--202, 1995.

\bibitem{ipm:Altman9}
A.~Altman.
\newblock Higher order primal--dual interior point method for separable convex
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\newblock {\em Control and Cybernetics (Poland)}, 25:761--772, 1996.

\bibitem{ipm:Altman6}
A.~Altman, M.~Amann, G.~Klaassen, A.~Ruszczynski, and W.~Sch{\"o}pp.
\newblock Cost--effective sulphur emission reduction under uncertainty.
\newblock {\em European Journal of Operational Research}, 90:395--412, 1996.

\bibitem{ipm:Altman2}
A.~Altman and J.~Gondzio.
\newblock {\em HOPDM} -- {A} higher order primal--dual method for large scale
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\newblock {Program Manual}, Systems Research Institute, Polish Academy of
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\newblock See also Altman and Gondzio \cite{ipm:Altman3}.

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A.~Altman and J.~Gondzio.
\newblock An efficient implementation of a higher order primal--dual interior
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\newblock {\em Archives of Control Sciences}, 2:23--40, 1993.

\bibitem{ipm:Altman3}
A.~Altman and J.~Gondzio.
\newblock {\em HOPDM} -- {A} higher order primal--dual method for large scale
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\newblock {\em European Journal of Operational Research}, 66:159--160, 1993.
\newblock See also Altman and Gondzio \cite{ipm:Altman2}, and Gondzio
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\bibitem{ipm:Altman10}
A.~Altman and J.~Gondzio.
\newblock Regularized symmetric indefinite systems in interior point methods
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\newblock {Logilab Technical Report} 98.6, Section of Management Studies,
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A.~Altman and K.~C. Kiwiel.
\newblock A note on some analytic center cutting plane methods for convex
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\newblock {\em Computational Optimization and Applications}, 5:175--180, 1996.

\bibitem{ipm:Amaya1}
J.~Amaya.
\newblock Numerical experiments with the symmetric affine scaling algorithm on
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\newblock {\em Optimization}, 27:51--62, 1993.

\bibitem{ipm:Amaya2}
J.~Amaya.
\newblock On the symmetric affine scaling algorithm for linear programming.
\newblock {\em Optimization}, 32:147--158, 1995.

\bibitem{ipm:Andersen7}
E.~D. Andersen.
\newblock Finding all linearly dependent rows in large--scale linear
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\newblock {\em Optimization Methods and Software}, 6:219--2227, 1995.

\bibitem{ipm:Andersen19}
E.~D. Andersen.
\newblock Implementation of interior point methods for large scale linear
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\newblock {Technical Report} 96--1, Department of Management, School of
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E.~D. Andersen.
\newblock On exploiting problem structure in a basis identification procedure
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\newblock {Technical Report} 96--6, Department of Management, School of
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\bibitem{ipm:Andersen16}
E.~D. Andersen.
\newblock {\em Solution of linear and convex optimization problems with
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\newblock PhD thesis, Department of Mathematics and Computer Science, Odense
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E.~D. Andersen.
\newblock The homogeneous self--dual methods for linear programming.
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E.~D. Andersen and K.~D. Andersen.
\newblock Presolving in linear programming.
\newblock {\em Mathematical Programming}, 71:221--245, 1995.

\bibitem{ipm:Andersen18}
E.~D. Andersen and K.~D. Andersen.
\newblock {The APOS LP solver}.
\newblock {Technical Report}, Center of Operations Research and Econometrics,
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\bibitem{ipm:Andersen20}
E.~D. Andersen and K.~D. Andersen.
\newblock {The APOS linear programming solver\,: An} implementation of the
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\newblock {CORE Discussion Paper} 9337, Center of Operations Research and
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\bibitem{ipm:Andersen24}
E.~D. Andersen and K.~D. Andersen.
\newblock A parallel interior--point algorithm for linear programming on a
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\newblock {CORE Discussion Paper} 9808, Center of Operations Research and
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\bibitem{ipm:Andersen25}
E.~D. Andersen and A.~Damgaard.
\newblock Utility based option pricing with proportional transaction costs and
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\newblock {Technical Report}, Department of Management, School of Business and
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\bibitem{ipm:Anderson15}
E.~D. Andersen, J.~Gondzio, C.~M{\'e}sz{\'a}ros, and X.~Xu.
\newblock Implementation of interior point methods for large scale linear
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\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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\bibitem{ipm:Andersen6}
E.~D. Andersen and Y.~Ye.
\newblock Combining interior--point algorithms and pivoting for linear
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\newblock {\em Management Science}, 42:1719--1731, 1996.

\bibitem{ipm:Andersen23}
E.~D. Andersen and Y.~Ye.
\newblock On a homogeneous algorithm for a monotone complementarity problem
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\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
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E.~D. Andersen and Y.~Ye.
\newblock A computational study of the homogeneous algorithm for large-- scale
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\newblock {\em Computational Optimization and Applications}, 10:243--269, 1998.

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E.~D. Andersen and Y.~Ye.
\newblock On a homogeneous algorithm for the monotone complementarity problem.
\newblock {\em Mathematical Programming}, 84:375--399, 1999.

\bibitem{ipm:Andersen5}
J.~A. Andersen.
\newblock {\em Iterative methods for the solution of linear programs}.
\newblock PhD thesis, Department of Mathematics and Statistics, Brunel
  University, Uxbridge, Middlesex~UB8\,3PH, United Kingdom, 1992.

\bibitem{ipm:Andersen4}
J.~A. Andersen, R.~Levkovitz, and G.~Mitra.
\newblock Adapting the interior point method for the solution of linear
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\newblock In O.~Balci, R.~Sharda, and S.~A. Zenios, editors, {\em Operations
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\bibitem{ipm:Andersen1}
J.~A. Andersen, R.~Levkovitz, G.~Mitra, and M.~Tamiz.
\newblock Adopting interior search algorithms for the solution of {LP}s for
  serial, coarse grain parallel and massively parallel computers.
\newblock {Talk held at the First International Symposium on Interior Point
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  Uxbridge, Middlesex~UB8~3PH, United Kingdom, January 1990.

\bibitem{ipm:Andersen2}
J.~A. Andersen and G.~Mitra.
\newblock Solving the {Newton} iteration step of the interior point method on
  massively parallel ({SIMD}) computer.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Department of Mathematics and Statistics, Brunel University, Uxbridge,
  Middlesex~UB8~3PH, United Kingdom, January 1991.

\bibitem{ipm:Andersen3}
K.~D. Andersen.
\newblock An infeasible dual affine scaling method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
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\bibitem{ipm:Andersen10}
K.~D. Andersen.
\newblock A large scaling implementation of the dual affine scaling algorithm.
\newblock Preprint, Department of Mathematics and Computer Science, Odense
  University, DK--5320~Odense~M, Denmark, 1993.
\newblock To appear in {\em Mathematical Programming Society Committee on
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\bibitem{ipm:Andersen17}
K.~D. Andersen.
\newblock An efficient {Newton} barrier method for minimizing a sum of
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\newblock {\em SIAM Journal on Optimization}, 6:74--95, 1996.

\bibitem{ipm:Andersen11}
K.~D. Andersen.
\newblock A modified {Schur} complement for handling dense columns in interior
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\newblock {\em ACM Transactions on Mathematical Software}, 22:348--356, 1996.

\bibitem{ipm:Andersen8}
K.~D. Andersen and E.~Christiansen.
\newblock Limit analysis with the dual affine scaling algorithm.
\newblock {\em Journal of Computational and Applied Mathematics}, 59:233--243,
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\bibitem{ipm:Andersen27}
K.~D. Andersen, E.~Christiansen, A.~R. Conn, and M.~L. Overton.
\newblock An efficient primal--dual interior--point method for minimizing a sum
  of {Euclidean} norms.
\newblock {CORE Discussion Paper}, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, August 1998.

\bibitem{ipm:Andersen12}
K.~D. Andersen and E.~D. Christiansen.
\newblock A {Newton} barrier method for minimizing a sum of {Euclidean} norms
  subject to linear equality constraints.
\newblock Preprint 95--07, Department of Mathematics and Computer Science,
  Odense University, DK--5320~Odense~M, Denmark, February 1995.

\bibitem{ipm:Andersen14}
K.~D. Andersen and E.~D. Christiansen.
\newblock A symmetric primal--dual {Newton} method for minimizing a sum of
  norms.
\newblock Preprint, Department of Mathematics and Computer Science, Odense
  University, DK--5320~Odense~M, Denmark, 1995.

\bibitem{ipm:Andrusenko1}
S.~K. Andrusenko, E.~A. Nurminskii, and P.~I. Stetsyuk.
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\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
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\newblock Folding the perfect corner.
\newblock {\em Time Magazin}, 124:55, December 3, 1984.

\bibitem{ipm:Anitescu2}
M.~Anitescu, G.~Lesaja, and F.~Potra.
\newblock Equivalence between different formulations of the linear
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\newblock {Reports on Computational Mathematics}~71, Department of Mathematics,
  University of Iowa, Iowa City, IA~52242, USA, June 1995.

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M.~Anitescu, G.~Lesaja, and F.~Potra.
\newblock An infeasible--interior--point predictor--corrector algorithm for the
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K.~M. Anstreicher.
\newblock Analysis of a modified {Karmarkar} algorithm for linear programming.
\newblock {Technical Report} B\#84, Yale School of Management, Yale University,
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K.~M. Anstreicher.
\newblock Analysis of {Karmarkar's} algorithm for fractional linear
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\newblock {Technical Report}, Yale School of Management, Yale University, New
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\bibitem{ipm:Anstreicher3}
K.~M. Anstreicher.
\newblock A monotonic projective algorithm for fractional linear programming.
\newblock {\em Algorithmica}, 1(4):483--498, 1986.

\bibitem{ipm:Anstreicher4}
K.~M. Anstreicher.
\newblock A strenghtened acceptance criterion for approximate projections in
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\newblock {\em Operations Research Letters}, 5:211--214, 1986.

\bibitem{ipm:Anstreicher5}
K.~M. Anstreicher.
\newblock On the complexity of the projective algorithm for standard form
  linear programming.
\newblock {Technical Report} B\#104, Yale School of Management, Yale
  University, New Haven, CT~06520, USA, 1987.

\bibitem{ipm:Anstreicher7}
K.~M. Anstreicher.
\newblock Linear programming and the {Newton} barrier flow.
\newblock {\em Mathematical Programming}, 41:367--373, 1988.

\bibitem{ipm:Anstreicher18}
K.~M. Anstreicher.
\newblock A combined phase\,{I}\,--\,phase\,{II} projective algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 43:209--223, 1989.

\bibitem{ipm:Anstreicher10}
K.~M. Anstreicher.
\newblock Progress in interior point algorithms since 1984.
\newblock {\em SIAM News}, 22:12--14, March 1989.

\bibitem{ipm:Anstreicher22}
K.~M. Anstreicher.
\newblock Recent developments in algorithms for linear programming.
\newblock {Talk held at the Third SIAM Conference on Optimization in Boston,
  MA, USA}, Yale School of Management, Yale University, New Haven, CT~06520,
  USA, April 1989.

\bibitem{ipm:Anstreicher9}
K.~M. Anstreicher.
\newblock The worst--case step in {Karmarkar's} algorithm.
\newblock {\em Mathematics of Operations Research}, 14:294--302, 1989.

\bibitem{ipm:Anstreicher6}
K.~M. Anstreicher.
\newblock Dual ellipsoids and degeneracy in the projective algorithm for linear
  programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 141--149. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Anstreicher12}
K.~M. Anstreicher.
\newblock A standard form variant and safeguarded linesearch for the modified
  {Karmarkar} algorithm.
\newblock {\em Mathematical Programming}, 47:337--351, 1990.

\bibitem{ipm:Anstreicher23}
K.~M. Anstreicher.
\newblock Advances in interior point methods for linear programming.
\newblock {Tutorial held at the ORSA/TIMS Joint National Meeting in Anaheim,
  CA, USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, November 1991.

\bibitem{ipm:Anstreicher11}
K.~M. Anstreicher.
\newblock A combined phase\,{I}\,--\,phase\,{II} scaled potential algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 52:429--439, 1991.

\bibitem{ipm:Anstreicher17}
K.~M. Anstreicher.
\newblock On monotonicity in the scaled potential algorithm for linear
  programming.
\newblock {\em Linear Algebra and Its Applications}, 152:223--232, 1991.

\bibitem{ipm:Anstreicher8}
K.~M. Anstreicher.
\newblock On the performance of {Karmarkar's} algorithm over a sequence of
  iterations.
\newblock {\em SIAM Journal on Optimization}, 1(1):22--29, 1991.

\bibitem{ipm:Anstreicher25}
K.~M. Anstreicher.
\newblock Efficient centering for linear programming interior point methods.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, January 1992.

\bibitem{ipm:Anstreicher20}
K.~M. Anstreicher.
\newblock On interior algorithms for linear programming with no regularity
  assumptions.
\newblock {\em Operations Research Letters}, 11:209--212, 1992.

\bibitem{ipm:Anstreicher16}
K.~M. Anstreicher.
\newblock Strict monotonicity and improved complexity in the standard form
  projective algorithm for linear programming.
\newblock {\em Mathematical Programming}, 62:517--535, 1993.

\bibitem{ipm:Anstreicher31}
K.~M. Anstreicher.
\newblock Large step volumetric potential reduction algorithms for linear
  programming.
\newblock {\em Annals of Operations Research}, 62:521--538, 1996.

\bibitem{ipm:Anstreicher19}
K.~M. Anstreicher.
\newblock On long step path following and {SUMT} for linear and quadratic
  programming.
\newblock {\em SIAM Journal on Optimization}, 6:33--46, 1996.

\bibitem{ipm:Anstreicher37}
K.~M. Anstreicher.
\newblock Potential reduction algorithms.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 125--158. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Anstreicher38}
K.~M. Anstreicher.
\newblock Ellipsoidal approximations of convex sets based on the volumetric
  barrier.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, March 1997.

\bibitem{ipm:Anstreicher36}
K.~M. Anstreicher.
\newblock {\em {Interior Point Methods in Theory and Practice}}, volume~76 of
  {\em Mathematical Programming}.
\newblock North Holland, Amsterdam, The Netherlands, 1997.
\newblock (Special issue).

\bibitem{ipm:Anstreicher32}
K.~M. Anstreicher.
\newblock On {Vaidya's} volumetric cutting plane method for convex programming.
\newblock {\em Mathematics of Operations Research}, 22:63--89, 1997.

\bibitem{ipm:Anstreicher33}
K.~M. Anstreicher.
\newblock Volumetric path following algorithms for linear programming.
\newblock {\em Mathematical Programming}, 76:245--263, 1997.

\bibitem{ipm:Anstreicher42}
K.~M. Anstreicher.
\newblock On the equivalence of convex programming bounds for {Boolean}
  quadratic programming.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, May 1998.

\bibitem{ipm:Anstreicher44}
K.~M. Anstreicher.
\newblock The volumetric barrier for convex quadratic constraints.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, October 1998.

\bibitem{ipm:Anstreicher40}
K.~M. Anstreicher.
\newblock The volumetric barrier for semidefinite programming.
\newblock {Technical Report}, Department of Mathematics, University of Iowa,
  Iowa City, IA~52242, USA, January 1998.

\bibitem{ipm:Anstreicher39}
K.~M. Anstreicher.
\newblock Towards a practical volumetric cutting plane method for convex
  programming.
\newblock {\em SIAM Journal on Optimization}, 9:190--206, 1999.

\bibitem{ipm:Anstreicher21}
K.~M. Anstreicher and R.~A. Bosch.
\newblock On partial updating in a potential reduction linear programming
  algorithm of {Kojima, Mizuno and Yoshise}.
\newblock {Technical Report}, Yale School of Management, Yale University, New
  Haven, CT~06520, USA, 1991.
\newblock Same as Bosch and Anstreicher \cite{ipm:Bosch2}.

\bibitem{ipm:Anstreicher13}
K.~M. Anstreicher and R.~A. Bosch.
\newblock Long steps in a ${O(n^{3}L)}$ algorithm for linear programming.
\newblock {\em Mathematical Programming}, 54:251--265, 1992.

\bibitem{ipm:Anstreicher30}
K.~M. Anstreicher and R.~A. Bosch.
\newblock A new infinity--norm path following algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:236--246, 1995.

\bibitem{ipm:Anstreicher35}
K.~M. Anstreicher and M.~Fampa.
\newblock A long--step path following algorithm for semidefinite programming
  problems.
\newblock In P.~M. Pardalos and M.~Wolkowicz, editors, {\em Topics in
  Semidefinite and Interior--Point Methods}, volume~18 of {\em Fields Institute
  Communications Series}, pages 181--196. American Mathematical Society (AMS),
  Providence, RI, USA, 1998.

\bibitem{ipm:Freund34}
K.~M. Anstreicher and R.~M. Freund.
\newblock Following a ''balanced'' trajectory from an infeasible point to an
  optimal linear programming solution with a polynomial--time algorithm.
\newblock {\em Mathematics of Operations Research}, 21:839--859, 1996.

\bibitem{ipm:Anstreicher34}
K.~M. Anstreicher and R.~M. Freund.
\newblock {\em {Interior Point Methods in Mathematical Programming}}, volume~62
  of {\em Annals of Operations Research}.
\newblock Baltzer Science Publishing Company, Basel, Switzerland, 1996.
\newblock Special issue.

\bibitem{ipm:Anstreicher15}
K.~M. Anstreicher, {D. den} Hertog, C.~Roos, and T.~Terlaky.
\newblock A long step barrier method for convex quadratic programming.
\newblock {\em Algorithmica}, 10:365--382, 1993.

\bibitem{ipm:Anstreicher24}
K.~M. Anstreicher and J.~Ji.
\newblock More on dual ellipsoids and degeneracy in interior algorithms for
  linear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, May 1992.

\bibitem{ipm:Anstreicher27}
K.~M. Anstreicher, J.~Ji, F.~A. Potra, and Y.~Ye.
\newblock Probabilistic analysis of an infeasible primal--dual algorithm for
  linear programming.
\newblock {Reports on Computational Mathematics}~27, Department of Mathematics,
  University of Iowa, Iowa City, IA~52242, USA, July 1992.

\bibitem{ipm:Anstreicher28}
K.~M. Anstreicher, J.~Ji, F.~A. Potra, and Y.~Ye.
\newblock Average performance of a self--dual interior--point algorithm for
  linear programming.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 1--15. World Scientific Publishing Co., London, United
  Kingdom, 1993.

\bibitem{ipm:Anstreicher26}
K.~M. Anstreicher, J.~Ji, and Y.~Ye.
\newblock Average performance of an ellipsoid termination criterion for linear
  programming interior point algorithms.
\newblock {Technical Report} 92--01, Department of Management Science,
  University of Iowa, Iowa City, IA~52242, USA, February 1992.

\bibitem{ipm:Anstreicher29}
K.~M. Anstreicher and J.-Ph. Vial.
\newblock On the convergence of an infeasible primal--dual interior--point
  method for convex programming.
\newblock {\em Optimization Methods and Software}, 3:273--283, 1994.

\bibitem{ipm:Anstreicher14}
K.~M. Anstreicher and P.~Watteyne.
\newblock A family of search directions for {Karmarkar's} algorithm.
\newblock {\em Operations Research}, 41:759--767, 1993.

\bibitem{ipm:Anstreicher41}
K.~M. Anstreicher and H.~Wolkowicz.
\newblock On {Lagrangian} relaxation of quadratic matrix constraints.
\newblock {Research Report} CORR 98--24, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario~N2L\,3G1, Canada,
  1998.

\bibitem{ipm:Arbel1}
A.~Arbel.
\newblock {\em {Exploring Interior Point Linear Programming\,: Algorithms and
  Software}}.
\newblock Foundations of Computing Series. MIT Press, Cambridge, MA~02142, USA,
  1993.

\bibitem{ipm:Arbel4}
A.~Arbel.
\newblock Generating interior search directions for multiobjective linear
  programming using approximate gradients and efficient anchoring points.
\newblock {\em Optimization}, 28:149--164, 1993.

\bibitem{ipm:Arbel2}
A.~Arbel.
\newblock An interior multiobjective linear programming algorithm.
\newblock {\em Computers and Operations Research}, 20(7):723--735, 1993.

\bibitem{ipm:Arbel12}
A.~Arbel.
\newblock Large--scale optimization methods applied to the cutting stock
  problem of irregular shapes.
\newblock {\em International Journal of Production Research}, 31:483--500,
  1993.

\bibitem{ipm:Arbel7}
A.~Arbel.
\newblock Using sequential generation of anchoring points in an interior
  multi--objective primal--dual linear programming algorithm.
\newblock {\em Archives of Control Sciences}, 2:5--21, 1993.

\bibitem{ipm:Arbel11}
A.~Arbel.
\newblock A weighted--gradient approach to multi--objective linear programming
  problems using the analytical hierarchy process.
\newblock {\em Mathematical Computations and Modelling}, 17(4--5):27--39, 1993.

\bibitem{ipm:Arbel3}
A.~Arbel.
\newblock Anchoring points and cones of opportunities in interior
  multiobjective linear programming.
\newblock {\em Journal of the Operational Research Society}, 45(1):83--96,
  1994.

\bibitem{ipm:Arbel9}
A.~Arbel.
\newblock Interior--point methods for multiobjective linear programming
  problems.
\newblock In G.~H.~Tzeng et~al., editor, {\em Multiple Criteria Decision
  Making, Proceedings of the 10th International Conference ''Expand and Enrich
  the Domain of Thinking and Application'', held at Taipei, Taiwan, July 1992},
  pages 27--36. Springer Verlag, Berlin, Germany, 1994.

\bibitem{ipm:Arbel5}
A.~Arbel.
\newblock An interior multiobjective primal--dual linear programming algorithm
  using approximated gradients and sequential generation of anchor points.
\newblock {\em Optimization}, 30:137--150, 1994.

\bibitem{ipm:Arbel8}
A.~Arbel.
\newblock A multiobjective interior primal--dual linear programming algorithm.
\newblock {\em Computers and Operations Research}, 21:433--445, 1994.

\bibitem{ipm:Arbel6}
A.~Arbel.
\newblock Using efficient anchoring points for generating search directions in
  interior multi--objective linear programming.
\newblock {\em Journal of the Operational Research Society}, 45:330--334, 1994.

\bibitem{ipm:Arbel13}
A.~Arbel.
\newblock An interior multiple objective primal--dual linear programming
  algorithm using efficient anchoring points.
\newblock {\em Journal of the Operational Research Society}, 46:1121--1132,
  1995.

\bibitem{ipm:Arbel17}
A.~Arbel.
\newblock An interior multiobjective primal--dual linear programming algorithm
  based on approximated gradients and efficient anchoring points.
\newblock {\em Computers and Operations Research}, 24:353--365, 1997.

\bibitem{ipm:Arbel16}
A.~Arbel and P.~Korhonen.
\newblock Using aspiration levels in an interactive interior multiobjective
  linear programming algorithm.
\newblock {\em European Journal of the Operational Research}, 89:193--201,
  1996.

\bibitem{ipm:Arbel18}
A.~Arbel and P.~Korhonen.
\newblock Using aspiration levels in an interior primal--dual multiobjective
  linear programming algorithm.
\newblock {\em Journal of Multi--Criteria Decisions and Analysis}, 5:61--71,
  1996.

\bibitem{ipm:Arbel15}
A.~Arbel and S.~S. Oren.
\newblock Generating interior search directions for multiobjective linear
  programming.
\newblock {\em Journal of Multi--Criteria Decisions and Analysis}, 2:73--86,
  1993.

\bibitem{ipm:Arbel10}
A.~Arbel and S.~S. Oren.
\newblock A modification of {Karmarkar's} algorithm for multiple objective
  linear programming.
\newblock In G.~H. Tzeng, editor, {\em Multiple Criteria Decision Making,
  Proceedings of the 10th International Conference ''Expand and Enrich the
  Domain of Thinking and Application'', held at Taipei, Taiwan, July 1992},
  pages 37--46. Springer Verlag, Berlin, Germany, 1994.

\bibitem{ipm:Arbel14}
A.~Arbel and S.~S. Oren.
\newblock Using approximate gradients in developing an interactive interior
  primal--dual multiobjective linear programming algorithm.
\newblock {\em European Journal of the Operational Research}, 89:202--211,
  1996.

\bibitem{ipm:Arbel19}
A.~Arbel and P.Korhonen.
\newblock An interior multiobjective linear programming algorithm using
  aspirations.
\newblock In G.~Fandel and T.~Gal, editors, {\em Multiple Criteria Decision
  Making, Proceedings of the Conference held at Hagen, Germany, 1995}, volume
  448 of {\em Lecture Notes in Economics and Mathematical Systems}, pages
  245--254. Springer Verlag, Berlin, Germany, 1997.

\bibitem{ipm:ArgaezRamos1}
M.~{Arg{\'a}ez Ramos}.
\newblock {\em Exact and inexact {Newton} linesearch interior--point algorithms
  for nonlinear programming problems}.
\newblock PhD thesis, Department of Computational and Applied Mathematics, Rice
  University, Houston, TX~77251, USA, 1997.
\newblock Available as\,: Technical Report TR97--13.

\bibitem{ipm:Armacost1}
A.~Armacost and S.~Mehrotra.
\newblock A computational comparison of the network simplex method with the
  dual affine scaling method.
\newblock {\em Journal of the Operational Research Society of India
  (Opsearch)}, 28(1):18--35, 1991.

\bibitem{ipm:Armand1}
P.~Armand, J.~C. Gilbert, and S.~Jan-J{\'e}gou.
\newblock A feasible {BFGS} interior point algorithm for solving strongly
  convex minimization problems.
\newblock {Research Report} 3500, Institute National de Recherche en
  Informatique et Automatique (INRIA), F--78153~Roquencourt, France, October
  1998.

\bibitem{ipm:Aronson1}
J.~Aronson, R.~Barr, R.~Helgason, J.~Kennington, A.~Loh, and H.~Zaki.
\newblock The projective transformation algorithm by {Karmarkar}\,: {A}
  computational experiment with assignment problems.
\newblock {Technical Report} 85--OR--3, Department of Operations Research,
  Southern Methodist University, Dallas, TX~75275, USA, August 1985.

\bibitem{ipm:Aronson2}
J.~Aronson, R.~Barr, R.~Helgason, J.~Kennington, A.~Loh, and H.~Zaki.
\newblock A specialization of {Karmarkar's} algorithm to solve network
  problems.
\newblock {Technical Report}, Department of Operations Research, Southern
  Methodist University, Dallas, TX~75275, USA, 1985.

\bibitem{ipm:Astfalk1}
G.~Astfalk, I.~J. Lustig, R.~E. Marsten, and D.~Shanno.
\newblock The interior--point method for linear programming.
\newblock {\em IEEE Software}, 9(4):61--68, 1992.

\bibitem{ipm:At1}
{The {AT~\&~T KORBX} Linear Programming System, AT~\&~T Bell Laboratories,
  Holmdel, NJ~07733, USA}, 1988.
\newblock Introduced at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA, October 1988.

\bibitem{ipm:Atkinson6}
D.~S. Atkinson.
\newblock {\em Scaling and interior--point methods in optimization}.
\newblock PhD thesis, Coordinated Science Laboratory, College of Engineering,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1992.

\bibitem{ipm:Atkinson3}
D.~S. Atkinson and P.~M. Vaidya.
\newblock An analytic center based cutting plane algorithm for convex
  programming.
\newblock {Technical Report}, College of Commerce and Business Administration,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, June
  1992.

\bibitem{ipm:Atkinson2}
D.~S. Atkinson and P.~M. Vaidya.
\newblock A cutting plane algorithm that uses analytic centers.
\newblock {Working Paper}, College of Commerce and Business Administration,
  University of Illinois at Urbana--Champaign, Urbana, IL~61820, USA, 1992.

\bibitem{ipm:Atkinson5}
D.~S. Atkinson and P.~M. Vaidya.
\newblock Minimizing weighted self--concordant logarithmic barrier functions by
  scaling.
\newblock {Preprint}, Department of Mathematics, University of Illinois at
  Urbana--Champaign, Urbana, IL~61820, USA, 1992.

\bibitem{ipm:Atkinson1}
D.~S. Atkinson and P.~M. Vaidya.
\newblock A scaling technique for finding the weighted analytic center of a
  polytope.
\newblock {\em Mathematical Programming}, 57:163--192, 1992.

\bibitem{ipm:Atkinson4}
D.~S. Atkinson and P.~M. Vaidya.
\newblock A cutting plane algorithm for convex programming that uses analytic
  centers.
\newblock {\em Mathematical Programming}, 69:1--43, 1995.

\bibitem{ipm:Asic4}
M.~D. A\u{s}i{\'c} and V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}.
\newblock An interior semi--infinite programming method.
\newblock {\em Journal of Optimization Theory and Applications}, 59:369--390,
  1988.

\bibitem{ipm:Asic8}
M.~D. A\u{s}i{\'c} and V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}.
\newblock Ill--conditionedness and interior--point methods.
\newblock {Technical Report}, Laboratory for Operations Research, Faculty of
  Organizational Sciences, University of Belgrade, Jove Ilica~154,
  YU--11040~Belgrade, Yugoslavia, February 1998.

\bibitem{ipm:Asic6}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Karmarkar algoritam\,: {Analiza} numericke stabilnosti i neke
  modifikacije.
\newblock {\em Proceedings of the 12th Yugoslav Symposium on Operations
  Research (Herceg--Novi, Yugoslavia, October 1985)}, pages 33--41, 1985.
\newblock (In Yugoslav).

\bibitem{ipm:Asic7}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Asimptotsko ponasanje {Karmarkarove} metode.
\newblock {\em Proceedings of the 13th Yugoslav Symposium on Operations
  Research (Herceg--Novi, Yugoslavia, October 1986)}, pages 81--88, 1986.
\newblock (In Yugoslav).

\bibitem{ipm:Asic3}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Asymptotic behavior and numerical stability of {Karmarkar's} method
  for linear programming.
\newblock {Technical Report}, University of Belgrade, Belgrade, Yugoslavia,
  1986.

\bibitem{ipm:Asic1}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Behavior of {Karmarkar's} method on degenerate problems.
\newblock {Technical Report}, Department of Mathematics, Michigan State
  University, East Lansing, MI~48824, USA, 1988.

\bibitem{ipm:Asic2}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock Asymptotic behavior of {Karmarkar's} method for linear programming.
\newblock {\em Mathematical Programming}, 46:173--190, 1990.

\bibitem{ipm:Asic5}
M.~D. A\u{s}i{\'c}, V.~V. Kova\u{c}evi{\'c}-Vuj\u{c}i{\'c}, and M.~D.
  Radosavljevi{\'c}-Nikoli{\'c}.
\newblock A note on limiting behavior of the projective and the affine
  rescaling algorithms.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 151--157. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Auslender1}
A.~Auslender and M.~Haddou.
\newblock An interior--proximal method for convex linearly constrained problems
  and its extension to variational inequalities.
\newblock {\em Mathematical Programming}, 71:77--100, 1995.

\bibitem{ipm:Babrovnikova1}
E.~Babrovnikova and S.~Vavasis.
\newblock Accurate solution of weighted least squares by iterative methods.
\newblock {Preprint} ANL/MSC--P644--0297, Mathematics and Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, February 1997.

\bibitem{ipm:Bach1}
R.~Bach.
\newblock {{\"U}ber die Effizienz eines polynomialen Verfahrens zur L{\"o}sung
  von linearen Optimierungsproblemen. (About the efficiency of a polynomial
  method for solving linear programming problems)}.
\newblock Master's thesis, {Fachbereich Wirtschaftswissenschaften und
  Operations Research, FernUniversit{\"a}t Hagen}, P. O. Box 940, D--5800
  Hagen, Germany, December 1990.
\newblock (In German).

\bibitem{ipm:Bachem1}
A.~Bachem and M.~Strietzel.
\newblock {Eine parallele Implementierung des Karmarkar--Verfahrens (A parallel
  implementation of Karmarkar's method)}.
\newblock {Technical Report} 92--121, Department of Mathematics, University of
  Cologne, Cologne, Germany, 1992.
\newblock (In German).

\bibitem{ipm:Bachem2}
A.~Bachem and M.~Strietzel.
\newblock {Einbettung der parallelen Grundsoftware CARO in die primale--duale
  Barrierfunktionsmethode (Imbedding of the parallel basic software CARO into
  the primal--dual barrier function method)}.
\newblock {Technical Report} 93--129, Department of Mathematics, University of
  Cologne, Cologne, Germany, 1993.
\newblock (In German).

\bibitem{ipm:Bagchi1}
A.~Bagchi and B.~Kalantari.
\newblock A method for computing approximate solution of the trust region
  problem with application to projective methods for quadratic programming.
\newblock {Working Paper}, Department of Computer Science, Rutgers University,
  New Brunswick, NJ~08903, USA, 1988.

\bibitem{ipm:Bahn1}
O.~Bahn, J.-L. Goffin, J.-Ph. Vial, and O.~Du Merle.
\newblock Implementation and behavior of an interior point cutting plane
  algorithm for convex programming\,: {An} application to geometric
  programming.
\newblock {Working Paper}, University of Geneva, Geneva, Switzerland, 1991.
\newblock See also Bahn et al.\,\cite{ipm:Bahn3}.

\bibitem{ipm:Bahn3}
O.~Bahn, J.-L. Goffin, J.-Ph. Vial, and O.~Du Merle.
\newblock Experimental behavior of an interior point cutting plane algorithm
  for convex programming\,:\,{An} application to geometric programming.
\newblock {\em Discrete Applied Mathematics}, 49:3--23, 1994.
\newblock See also Bahn et al.\,\cite{ipm:Bahn1}.

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\newblock {Technical Annex} T--2.3.2, Faculty of Technical Mathematics and
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\newblock {Technical Report} OTC\,97/06, Optimization Technology Center,
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\newblock {\em Management Science}, 34:1472--1479, 1988.

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\newblock {Technical Report} 91--7, Department of Industrial and Operations
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R.~Conway and M.~Magazine.
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G.~B. Dantzig, D.~Goldfarb, E.~Lawler, C.~Monma, and S.~M. Robinson.
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\newblock Containing\,: B.~Kahin, The case against {''software patents''},
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G.~B. Dantzig, D.~Goldfarb, E.~Lawler, C.~Monma, and S.~M. Robinson.
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J.~E. Dennis, M.~Heinkenschloss, and L.~N. Vicente.
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J.~E. Dennis, M.~Heinkenschloss, and L.~N. Vicente.
\newblock {TRICE}\,--\,{Trust--region} interior--point algorithms for optimal
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\newblock {Project}, Department of Computational and Applied Mathematics, Rice
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J.~E. Dennis, M.~Heinkenschloss, and L.~N. Vicente.
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J.~E. Dennis, A.~M. Morshedi, and K.~Turner.
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Z.~Y. Diao.
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\newblock A remark on {Karmarkar's} algorithm.
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\newblock Interior point algorithms and dynamic systems.
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\newblock Some remarks on {Karmarkar's} potential function.
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\newblock Iterative solution of problems of linear and quadratic programming.
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\newblock On the convergence of an iterative process.
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I.~I. Dikin.
\newblock Letter to the editor.
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I.~I. Dikin.
\newblock The convergence of dual variables.
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I.~I. Dikin.
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I.~I. Dikin and C.~Roos.
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I.~I. Dikin and V.~I. Zorkaltsev.
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J.~Ding.
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\newblock {Technical Report}, University of Southern Mississippi, USA, 1992.
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J.~Ding.
\newblock A scaled gradient projection algorithm for linear complementarity
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\newblock Incorrect author name, see Ding \cite{ipm:Ding4}.

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N.~F. Dinn, N.~K. Karmarkar, and L.~P. Sinha.
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M.~H. Dodani and A.~J.~G. Babu.
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\newblock {\em Computers and Industrial Engineering}, 13:285--289, 1987.

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M.~H. Dodani and A.~J.~G. Babu.
\newblock Karmarkar's projective method for linear programming\,: {A}
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\newblock {\em Computers and Industrial Engineering}, 16:198--206, 1989.

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M.~H. Dodani and A.~J.~G. Babu.
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\newblock Springer Verlag, Berlin, Germany, 1989.

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P.~D. Domich, P.~T. Boggs, J.~R. Donaldson, and C.~Witzgall.
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P.~D. Domich, P.~T. Boggs, J.~R. Donaldson, and C.~Witzgall.
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P.~D. Domich, P.~T. Boggs, J.~R. Donaldson, and C.~Witzgall.
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P.~D. Domich, P.~T. Boggs, J.~E. Rogers, and C.~Witzgall.
\newblock Optimizing over 3--d subspaces in an interior point method.
\newblock {\em Linear Algebra and Its Applications}, 152:315--342, 1991.

\bibitem{ipm:Doup1}
T.~Doup, R.~Bisseling, and L.~Loyens.
\newblock A parallel interior point algorithm for linear programming on a
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\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
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\newblock See also Bisseling, Doup and Loyens\,\cite{ipm:Bisseling1}.

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M.~L. Dowling.
\newblock Comparing the affine and projective vector fields associated with
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\newblock {Technical Report}, Department of Management, University of Georgia,
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\newblock Submitted to {\em Mathematical Programming}.

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M.~L. Dowling.
\newblock An affine scaling method for nonlinear programming.
\newblock {Habilitationthesis}, Institut f{\"u}r Angewandte Mathematik,
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M.~L. Dowling.
\newblock An affine scaling algorithm for linear programming problems with
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\newblock {\em Mathematical Models of Operations Research}, 43:301--318, 1996.

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\newblock Why is the objective function nonlinearized in the interior point
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\newblock {\em Mathematics in Practice and Theory}, 2:63--68, 1990.
\newblock (In Chinese).

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\newblock The solution of large--scale least--squares problems on
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\bibitem{ipm:Zhang24}
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\newblock {Technical Report} TR~97--19, Department of Computational and Applied
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\bibitem{ipm:Eckstein1}
J.~Eckstein, R.-J. Qi, V.~I. Ragulin, and S.~A. Zenios.
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\newblock {Technical Report} TMC--230, Thinking Machines Corporation,
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\newblock Also available as Decision Sciences Department Report~92--05--06, The
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\bibitem{ipm:Economist1}
Not so simplex.
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C.~Edirisinghe and W.~Ziemba.
\newblock A boundary point algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
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  British Columbia, Vancouver, BC~V6T~1Y8, Canada, November 1991.

\bibitem{ipm:Edwards1}
J.~J. Edwards and J.~A. Tomlin.
\newblock Towards a highly parallel mathematical programming system.
\newblock {Talk held at the 14th International Mathematical Programming
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\newblock {Technical Report in preparation}.

\bibitem{ipm:ElBakry4}
A.~S. {El--Bakry}.
\newblock {\em On the role of indicators in identifying zero variables in
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\newblock PhD thesis, Department of Mathematical Sciences, Rice University,
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\bibitem{ipm:ElBakry8}
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\newblock {\em Optimization Methods and Software}, 9:37--44, 1998.

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A.~S. {El--Bakry}, R.~A. Tapia, T.~Tsuchiya, and Y.~Zhang.
\newblock On the formulation and theory of the {Newton} interior--point method
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\newblock {\em Journal of Optimization Theory and Applications}, 89:507--541,
  1996.

\bibitem{ipm:ElBakry2}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock Numerical comparisons of local convergence strategies for
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\newblock {Technical Report} TR~91--18, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:ElBakry3}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock On obtaining highly accurate or basic solutions using interior--point
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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  TX~77251, USA, May 1992.

\bibitem{ipm:ElBakry7}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock Logarithmic indicators and the identification of subgroups of
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\newblock {Technical Report} TR~93--35, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, September 1993.

\bibitem{ipm:ElBakry1}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock A study of indicators for identifying zero variables in
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\newblock {\em SIAM Review}, 36:45--72, 1994.

\bibitem{ipm:ElBakry5}
A.~S. {El--Bakry}, R.~A. Tapia, and Y.~Zhang.
\newblock On the convergence rate of {Newton} interior--point methods in the
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\newblock {\em Computational Optimization and Applications}, 6:157--167, 1996.

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A.~Emmett.
\newblock Karmarkar's algorithm\,: {A} threat to simplex~?
\newblock {\em IEEE Spectrum}, 22(12):54--55, December 1985.

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T.~J. Encheva.
\newblock Computational comparisons for the method of centers of gravity of
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\newblock {\em Serdica (Bulgaricae Mathematicae Publicationes)},
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\bibitem{ipm:Epelman1}
M.~Epelman and R.~M. Freund.
\newblock Condition number complexity of an elementary algorithm for resolving
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\newblock {Technical Report}, Sloan School of Management, Massachusetts
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\newblock {Technical Report}, Sloan School of Management, Massachusetts
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\bibitem{ipm:Eriksson1}
J.~R. Eriksson.
\newblock Algorithms for entropy and mathematical programming.
\newblock {Link{\"o}ping Studies in Science and Technology Dissertations}~63,
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\newblock An iterative primal--dual algorithm for linear programming.
\newblock {Technical Report} LiTH--MAT--R--1985--10, Department of Mathematics,
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\bibitem{ipm:Eriksson3}
J.~R. Eriksson.
\newblock Using the entropy function to get an interior point method for linear
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\newblock {Technical Report} LiTH--MAT--R--1990--02, Department of Mathematics,
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\bibitem{ipm:Evtushenko3}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock {Barrier--Newton} methods in linear programming.
\newblock In J.~Henry and J.~P. Yvon, editors, {\em System Modelling and
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\bibitem{ipm:Evtushenko4}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Stable barrier--projection and barrier--{Newton} methods for linear
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\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
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\newblock See also Evtushenko and Zhadan
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\bibitem{ipm:Evtushenko1}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Stable barrier--projection and barrier--{Newton} methods in linear
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\newblock {\em Computational Optimization and Applications}, 3:289--303, 1994.
\newblock See also Evtushenko and Zhadan \cite{ipm:Evtushenko4}.

\bibitem{ipm:Evtushenko2}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Stable barrier--projection and barrier--{Newton} methods in nonlinear
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\newblock {\em Optimization Methods and Software}, 3:237--256, 1994.
\newblock See also Evtushenko and Zhadan \cite{ipm:Evtushenko4}.

\bibitem{ipm:Evtushenko5}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock Dual barrier--projection methods in linear programming.
\newblock In R.~P. Agarwal, editor, {\em Recent Trends in Optimization Theory
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\bibitem{ipm:Evtushenko7}
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\newblock Dual barrier--projection and {barrier--Newton} methods for linear
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\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
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\newblock (In Russian).

\bibitem{ipm:Evtushenko8}
Yu.~G. Evtushenko and V.~G. Zhadan.
\newblock On some papers on interior point methods.
\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
  (Moscow)}, 36(12):161--162, 1996.
\newblock (In Russian).

\bibitem{ipm:Evtushenko6}
Yu.~G. Evtushenko, V.~G. Zhadan, and A.~P. Cherenkov.
\newblock Application of {Newton's} method to the solution of linear
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\newblock {\em Zhurnal Vychislitel'noi Matematiki~i~ Matematicheskoi Fiziki
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\newblock Translated in\,: {\em USSR Computational Mathematics and Mathematical
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\bibitem{ipm:Ezzine1}
J.~Ezzine and M.~Ben-Daya.
\newblock Singular pertubed nonlinear {ODE}s and interior point optimization
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\newblock {\em Proceedings of the 1995 American Control Conference (Seattle,
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\bibitem{ipm:Fan2}
M.~K.~H. Fan.
\newblock A second--order interior point method for solving linear matrix
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\newblock {\em SIAM Journal on Control and Optimization}, 19\,?
\newblock (To appear).

\bibitem{ipm:Fan1}
M.~K.~H. Fan and B.~Nekooie.
\newblock A second--order interior point method for solving linear matrix
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\newblock {\em Proceedings of the 1994 American Control Conference (Baltimore,
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\newblock A different title found\,: {\em An algorithm on minimizing
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\bibitem{ipm:Fang10}
S.-C. Fang.
\newblock Dynamic facility network planning -- {A} solution architecture with
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\newblock {Technical Memorandum} 54112--860305--01~TM, AT~\&~T Bell
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\bibitem{ipm:Fang9}
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\newblock Dynamic facility network planning -- {An LP} loader.
\newblock {Technical Memorandum} 54112--860610--01~TM, AT~\&~T Bell
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\bibitem{ipm:Fang3}
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\newblock A new unconstrained convex programming approach to linear
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\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
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\bibitem{ipm:Fang4}
S.-C. Fang and S.~Puthenpura.
\newblock {\em Linear Optimization and Extensions}.
\newblock Prentice Hall, Englewood Cliffs, NJ~07632, USA, 1993.

\bibitem{ipm:Fang2}
S.-C. Fang, S.~C. Puthenpura, R.~Saigal, and P.~Sinha.
\newblock Stochastic linear programming via affine scaling and {Kalman}.
\newblock {Technical Memorandum} 51173--900808--01~TM, AT~\&~T Bell
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\bibitem{ipm:Fang12}
S.-C. Fang and L.~A. Slutsman.
\newblock Dynamic facility network planning -- {Modeling}.
\newblock {Technical Memorandum} 54112--850915--01~TM, AT~\&~T Bell
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\bibitem{ipm:Fang11}
S.-C. Fang and L.~A. Slutsman.
\newblock Dynamic facility network planning -- {Design} architecture.
\newblock {Technical Memorandum} 54112--860226--01~TM, AT~\&~T Bell
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\bibitem{ipm:Fang13}
S.-C. Fang and H.~S.~J. Tsao.
\newblock On the entropic perturbation and exponential penalty methods for
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\newblock {\em Journal of Optimization Theory and Applications}, 89:461--466,
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\bibitem{ipm:Fang5}
S.-C. Fang and J.~H.~S. Tsao.
\newblock Linear programming with an entropic perturbation.
\newblock {OR Research Report} 259, Operations Research Program, North Carolina
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\newblock To appear in {\em Zeitscrift f{\"u}r Operations Research -- Methods
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\bibitem{ipm:Fang6}
S.-C. Fang and J.~H.~S. Tsao.
\newblock An unconstrained convex programming approach to solving convex
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\newblock {OR Research Report} 263, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, April 1992.
\newblock To appear in {\em Optimization, 1992}.

\bibitem{ipm:Fang8}
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\newblock Entropic path--following for linear semi--infinite programming.
\newblock {OR Research Report} 266, Operations Research Program, North Carolina
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\bibitem{ipm:Fang7}
S.-C. Fang and S.-Y. Wu.
\newblock An inexact approach to solving linear semi--infinite programming
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\newblock {OR Research Report} 265, Operations Research Program, North Carolina
  State University, Raleigh, NC~27695, USA, November 1992.

\bibitem{ipm:Fang1}
W.~Fang and W.~Shi-Quan.
\newblock New algorithms for linear programming.
\newblock {Technical Report}, Institute of Applied Mathematics, Academia
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\bibitem{ipm:Farrell1}
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\newblock Recent advances in linear programming applied to global defense.
\newblock {\em Proceedings of the 27th IEEE Conference on Decision and Control,
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\bibitem{ipm:Fask1}
A.~Fask and W.~F. Walker.
\newblock A polynomial--time algorithm for solving transportation problems
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\newblock {Talk held at ORSA/TIMS Joint National Meeting in New Orleans, USA},
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\bibitem{ipm:Faybusovich9}
F.~Faybusovich.
\newblock On the phase portrait of the {Karmarkar's} flow.
\newblock In K.~L. Bowers, editor, {\em Computation and Control\,III
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\bibitem{ipm:Faybusovich1}
L.~E. Faybusovich.
\newblock Interior--point methods and entropy.
\newblock {\em Proceedings of the 30th IEEE Conference on Decision and Control
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\bibitem{ipm:Faybusovich2}
L.~E. Faybusovich.
\newblock Dikin's algorithm for matrix linear programming problems.
\newblock In J.~Henry and J.~P. Yvon, editors, {\em System Modelling and
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\bibitem{ipm:Faybusovich6}
L.~E. Faybusovich.
\newblock The {Gibbs} variational principle, gradient floes and interior--point
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\newblock In A.~Bloch, editor, {\em Hamiltonian and Gradient Flows, Algorithms
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\bibitem{ipm:Faybusovich3}
L.~E. Faybusovich.
\newblock A {Hamiltonian} structure for generalized affine--scaling vector
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\newblock {\em Journal on Nonlinear Sciences}, 5:11--28, 1995.

\bibitem{ipm:Faybusovich7}
L.~E. Faybusovich.
\newblock Jordan algebras, symmetric cones and interior--point methods.
\newblock {Research Report}, Department of Mathematics, University of Notre
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\bibitem{ipm:Faybusovich5}
L.~E. Faybusovich.
\newblock On a matrix generalization of affine--scaling vector fields.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 16:886--897,
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\bibitem{ipm:Faybusovich11}
L.~E. Faybusovich.
\newblock Linear systems in jordan algebras and primal--dual interior--point
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\newblock {Research Report}, Department of Mathematics, University of Notre
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\bibitem{ipm:Faybusovich8}
L.~E. Faybusovich.
\newblock Semidefinite programming\,: {A} path--following algorithm for a
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\newblock {\em SIAM Journal on Optimization}, 6:1007--1024, 1996.

\bibitem{ipm:Faybusovich13}
L.~E. Faybusovich.
\newblock {Euclidean Jordan} algebras and interior--point methods.
\newblock {Research Report}, Department of Mathematics, University of Notre
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\bibitem{ipm:Faybusovich14}
L.~E. Faybusovich.
\newblock Euclidean jordan algebras and generalized affine--scaling vector
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\newblock {Research Report}, Department of Mathematics, University of Notre
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\bibitem{ipm:Faybusovich12}
L.~E. Faybusovich.
\newblock Infinite--dimensional semidefinite programming\,: {Regularized}
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\newblock In P.~M. Pardalos and M.~Wolkowicz, editors, {\em Topics in
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\bibitem{ipm:Faybusovich15}
L.~E. Faybusovich.
\newblock A {Jordan}--algebraic approach to potential--reduction algorithms.
\newblock {Research Report}, Department of Mathematics, University of Notre
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\bibitem{ipm:Faybusovich4}
L.~E. Faybusovich and J.~B. Moore.
\newblock Infinite--dimensional quadratic optimization\,: {Interior}--point
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\newblock {\em Applied Mathematics and Optimization}, 36:43--66, 1997.

\bibitem{ipm:Faybusovich10}
L.~E. Faybusovich and J.~B. Moore.
\newblock Long step path--following algorithm for the convex quadratic
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\newblock {\em Journal of Optimization Theory and Applications}, 95:615--636,
  1997.
\newblock Also published in\,: {\em Proceedings of the 34th IEEE Conference on
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\bibitem{ipm:Feijoo2}
B.~Feijoo, A.~Sanchez, and C.~C. Gonzaga.
\newblock Interior post--optimality techniques for linear programming\,:
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\newblock {Working Paper}, Departamento de Matematicas Puras y Aplicadas,
  Universidad Simon Bolivar, Apartado Postal~89000, Caracas~1080~A, Venezuela,
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\bibitem{ipm:Feijoo1}
B.~Feijoo, A.~Sanchez, and C.~C. Gonzaga.
\newblock Maintaining closeness to the analytic center of a polytope by
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\newblock {\em Applied Mathematics and Optimization}, 35:139--144, 1997.

\bibitem{ipm:Feng1}
G.~Feng and B.~Yu.
\newblock Combined homotopy interior point method for nonlinear programming
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\newblock In T.~Ushijima, editor, {\em Advances in Numerical Mathematics
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\bibitem{ipm:Fernandes1}
L.~Fernandes, J.~J. J{\'u}dice, and J.~Patricio.
\newblock An investigation of interior--point and block pivoting algorithms for
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\newblock {\em Computational Optimization and Applications}, 5:49--77, 1996.

\bibitem{ipm:Ferris1}
M.~C. Ferris and A.~B. Philpott.
\newblock On the performance of {Karmarkar's} algorithm.
\newblock {\em Journal of the Operational Research Society}, 39:257--270, 1988.

\bibitem{ipm:Ferris2}
M.~C. Ferris and A.~B. Philpott.
\newblock An interior point algorithm for semi--infinite linear programming.
\newblock {\em Mathematical Programming}, 43:257--276, 1989.

\bibitem{ipm:Ferris3}
M.~C. Ferris and A.~B. Philpott.
\newblock On affine scaling and semi--infinite programming.
\newblock {\em Mathematical Programming}, 52:361--364, 1992.

\bibitem{ipm:Fiacco1}
A.~V. Fiacco.
\newblock Barrier methods in nonlinear programming.
\newblock In A.~Holzman, editor, {\em Operations Research Support Methodology},
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\newblock {\em Annals of Operations Research}, 27:371--380, 1990.

\bibitem{ipm:Fiacco5}
A.~V. Fiacco.
\newblock Objective function and logarithmic barrier function properties in
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\newblock {\em Optimization}, 34:213--222, 1995.

\bibitem{ipm:Fiacco4}
A.~V. Fiacco and J.~Lin.
\newblock Extension of algorithmic sensitivity calculations in nonlinear
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\newblock {Technical Report}, School of Engineering and Applied Science,
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\newblock To appear in {\em Optimization}.

\bibitem{ipm:Fiacco3}
A.~V. Fiacco and G.~P. McCormick.
\newblock {\em Nonlinear Programming\,: Sequential Unconstrained Minimization
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\newblock John Wiley \& Sons, New York, 1968.
\newblock Reprint\,: Volume 4 of {\em SIAM Classics in Applied Mathematics},
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\newblock On the local superlinear convergence of {Newton}--type method for
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\newblock {\em Optimization Methods and Software}, 6:83--107, 1995.

\bibitem{ipm:Facchinei1}
F.~Facchineiand~A. Fischer and C.~Kanzow.
\newblock On the identification of zero variables in an interior--point
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\newblock {Mathematical Programming Technical Report}, Department of Computer
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\newblock {\em Practical Methods of Optimization}, chapter 8.7\,: {Polynomial}
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\newblock John Wiley\,\&\,Sons, New York, second edition, 1987.

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\newblock Recent developments in linear and quadratic programming.
\newblock In A.~Iserles and M.~J.~D. Powell, editors, {\em The
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\newblock An interior point method for multifacility location problems with
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\newblock {Ergebnisberichte Angewandte Mathematik} 142, Institut f{\"u}r
  Mathematik, Universit{\"a}t Dortmund, Vogelpothsweg~64, Dortmund, Germany,
  1997.

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J.~J.~H. Forrest and J.~A. Tomlin.
\newblock Vector processing in simplex and interior methods for linear
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\newblock {\em Annals of Operations Research}, 22:71--100, 1990.

\bibitem{ipm:Forrest2}
J.~J.~H. Forrest and J.~A. Tomlin.
\newblock Implementing interior point linear programming methods in the
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\newblock {\em IBM Systems Journal}, 31(1):26--38, 1992.

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\newblock On linear least--squares problems with diagonally dominant weight
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\newblock {Technical Report} {TRITA--MAT--1995--OS2}, Optimization and Systems
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  Stockholm, Sweden, 1995.

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A.~L. Forsgren.
\newblock Optimality conditions for nonconvex semidefinite programming.
\newblock {Technical Report} {TRITA--MAT--1998--OS6}, Optimization and Systems
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  Stockholm, Sweden, May 1998.

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A.~L. Forsgren and P.~E. Gill.
\newblock Primal-dual interior methods for nonconvex nonlinear programming.
\newblock {\em SIAM Journal on Optimization}, 8:1132--1152, 1998.

\bibitem{ipm:Forsgren3}
A.~L. Forsgren, P.~E. Gill, and J.~R. Shinnerl.
\newblock Stability of symmetric ill--conditioned systems arising in interior
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\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 17:187--211,
  1996.

\bibitem{ipm:Forsgren1}
A.~L. Forsgren and W.~Murray.
\newblock Newton methods for large--scale linear equality--constrained
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\newblock {Technical Report} SOL~90--6, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, 1990.

\bibitem{ipm:Fourer1}
R.~Fourer and S.~Mehrotra.
\newblock Performance of an augmented system approach for solving
  least--squares problems in an interior--point method for linear programming.
\newblock {Technical Report (in preparation)}, Department of Industrial
  Engineering and Management Sciences, Northwestern University, Evanston,
  IL~60208, USA, 1991.

\bibitem{ipm:Fourer2}
R.~Fourer and S.~Mehrotra.
\newblock Performance of an augmented system approach for solving
  least--squares problems in an interior--point method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:26--31, August 1991.

\bibitem{ipm:Fourer3}
R.~Fourer and S.~Mehrotra.
\newblock Solving symmetric indefinite systems in an interior--point method for
  linear programming.
\newblock {\em Mathematical Programming}, 62:15--39, 1993.

\bibitem{ipm:Fragniere1}
E.~Fragniere, J.~Gondzio, and R.Sarkissian.
\newblock Structure exploiting tool in algebraic modeling languages.
\newblock {Technical Report} 1997.2, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, June 1997.

\bibitem{ipm:Fragniere2}
E.~Fragniere, J.~Gondzio, and J.-Ph. Vial.
\newblock A planning model with one million scenarios solved on an affordable
  parallel machine.
\newblock {Logilab Technical Report} 1998.11, Department of Management Studies,
  University of Geneva, 102 Bd Carl Vogt, CH--1211 Geneva, Switzerland, June
  1998.

\bibitem{ipm:Fraley4}
C.~Fraley.
\newblock Computational aspects of some projective methods for linear
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\newblock {Working Paper}, COMIN, University of Geneva, 2~Rue de Candolle,
  CH--1211~Geneva~4, Switzerland, 1988.

\bibitem{ipm:Fraley1}
C.~Fraley.
\newblock Linear updates for a single\,--\,phase projective method.
\newblock {\em Operations Research Letters}, 9:169--174, 1990.

\bibitem{ipm:Fraley3}
C.~Fraley and J.-Ph. Vial.
\newblock Numerical study of projective methods for linear programming.
\newblock In S.~Dolecki, editor, {\em Optimization\,: Proceedings of the 5th
  French--German Conference in Castel--Novel, Varetz, France, October 1988},
  volume 1405 of {\em Lecture Notes in Mathematics}, pages 25--38. Springer
  Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Fraley2}
C.~Fraley and J.-Ph. Vial.
\newblock Single\,--\,phase versus multiple\,--\,phase projective methods for
  linear programming.
\newblock {Technical Report}, COMIN, University of Geneva, 2~Rue de Candolle,
  CH--1211~Geneva~4, Switzerland, 1989.

\bibitem{ipm:Fraley5}
C.~Fraley and J.-Ph. Vial.
\newblock Alternative approaches to feasibility in projective methods for
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\newblock {\em ORSA Journal on Computing}, 4:285--299, 1992.

\bibitem{ipm:Franklin1}
J.~Franklin.
\newblock Convergence in {Karmarkar's} algorithm for linear programming.
\newblock {\em SIAM Journal on Numerical Analysis}, 24:928--945, 1987.

\bibitem{ipm:Freedman2}
B.~A. Freedman, S.~C. Puthenpura, and L.~P. Sinha.
\newblock A new {Karmarkar}--based algorithm for optimizing convex, nonlinear
  functions with linear constraints.
\newblock {Technical Report}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733,
  USA, 1988.

\bibitem{ipm:Freedman1}
B.~A. Freedman, S.~C. Puthenpura, and L.~P. Sinha.
\newblock A new affine scaling based algorithm for optimizing convex, nonlinear
  functions with linear constraints.
\newblock {Technical Report}, AT~\&~T Bell Laboratories, Holmdel, NJ~07733,
  USA, 1990.

\bibitem{ipm:Frenk1}
J.~B.~G. Frenk, J.~F. Sturm, and S.~Zhang.
\newblock An interior--point subgradient method for linearly constrained
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\newblock {\em Optimization Methods and Software}, 10:197--215, 1998.

\bibitem{ipm:Freund1}
R.~M. Freund.
\newblock An analogous of {Karmarkar's} algorithm for inequality constrained
  linear programs, with a 'new' class of projective transformations for
  centering a polytope.
\newblock {\em Operations Research Letters}, 7:9--13, 1988.

\bibitem{ipm:Freund3}
R.~M. Freund.
\newblock A generalization/extension of {Karmarkar's} algorithm for inequality
  constrained linear programs based on projective centering of the polyhedra.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, April 1988.

\bibitem{ipm:Freund4}
R.~M. Freund.
\newblock Projective transformations for finding the w--center of a polyhedra.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, October 1988.

\bibitem{ipm:Freund22}
R.~M. Freund.
\newblock Projective transformations for interior point algorithms.
\newblock {Talk held at the AMS--ISM--SIAM Research Conference on
  ''Mathematical Developments Arising from Linear Programming'' in Bowdoin
  College, Brunswick, Maine, USA}, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, June 1988.

\bibitem{ipm:Freund5}
R.~M. Freund.
\newblock Projective transformations for interior point methods, {Part\,I\,:
  Basic} theory and linear programming.
\newblock {Working Paper} 2049--88, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, October 1988.

\bibitem{ipm:Freund6}
R.~M. Freund.
\newblock Projective transformations for interior point methods, {Part\,II\,:
  Analysis} of an algorithm for finding the weighted center of a polyhedral
  system.
\newblock {Working Paper} 2050--88, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, October 1988.

\bibitem{ipm:Freund17}
R.~M. Freund.
\newblock Projective transformations for interior point algorithms, a
  superlinearly convergent algorithm for the w--center problem.
\newblock {Working Paper}, Sloan School of Management, Massachusetts Institute
  of Technology, Cambridge, MA~02139, USA, 1989.
\newblock To appear in {\em Mathematical Programming}.

\bibitem{ipm:Freund10}
R.~M. Freund.
\newblock Interior point algorithms for solving a linear program directly from
  an infeasible 'warm start'.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, May 1990.

\bibitem{ipm:Freund12}
R.~M. Freund.
\newblock Newton's method for general parametric center problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, October 1990.

\bibitem{ipm:Freund11}
R.~M. Freund.
\newblock Recent results and perspectives on solving linear programming from an
  infeasible 'warm start'.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, Sloan
  School of Management, Massachusetts Institute of Technology, Cambridge,
  MA~02139, USA, July 1990.

\bibitem{ipm:Freund9}
R.~M. Freund.
\newblock Theoretical efficiency of solving a linear program from an infeasible
  'warm start'.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Sloan School of Management, Massachusetts Institute of
  Technology, Cambridge, MA~02139, USA, January 1990.

\bibitem{ipm:Freund24}
R.~M. Freund.
\newblock Algorithms for solving a linear program from infeasible warm start
  based on the intuitive geometrics of {LP}.
\newblock {Talk held at the 14th International Mathematical Programming
  Symposium in Amsterdam, The Netherlands}, Sloan School of Management,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, August 1991.

\bibitem{ipm:Freund18}
R.~M. Freund.
\newblock A combined {phase\,I\,--\,phase\,II} algorithm for {LP} based on the
  intuitive geometry of linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, November 1991.

\bibitem{ipm:Freund23}
R.~M. Freund.
\newblock Computational complexity of tracing the path of centers of a linear
  inequality system as the data for the system is parametrically deformed.
\newblock {Talk held at the Workshop on Complexity Issues for Numerical
  Optimization, Cornell University, Ithaca, NY, USA}, Sloan School of
  Management, Massachusetts Institute of Technology, Cambridge, MA~02139, USA,
  March 1991.

\bibitem{ipm:Freund16}
R.~M. Freund.
\newblock Interior--point methods for linear programming\,: {A} status report.
\newblock {Tutorial held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Sloan School of Management, Massachusetts Institute of
  Technology, Cambridge, MA~02139, USA, May 1991.

\bibitem{ipm:Freund2}
R.~M. Freund.
\newblock Polynomial--time algorithms for linear programming based only on
  primal scaling and projected gradients of a potential function.
\newblock {\em Mathematical Programming}, 51:203--222, 1991.

\bibitem{ipm:Freund8}
R.~M. Freund.
\newblock A potential--function reduction algorithm for solving a linear
  program directly from an infeasible 'warm start'.
\newblock {\em Mathematical Programming}, 52:441--466, 1991.

\bibitem{ipm:Freund25}
R.~M. Freund.
\newblock Solving a linear program from an infeasible warm start\,:
  {Conceptual} issues, theory, and a new interior point algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, November 1991.

\bibitem{ipm:Freund7}
R.~M. Freund.
\newblock Theoretical efficiency of a shifted barrier function algorithm for
  linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:19--41, 1991.

\bibitem{ipm:Freund26}
R.~M. Freund.
\newblock Following a trajectory from an infeasible point to an optimal linear
  programming solution.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, May 1992.

\bibitem{ipm:Freund19}
R.~M. Freund.
\newblock Pre--selection of the {phase\,I\,--\,phase\,II} balance in a
  path--following algorithm for the 'warm start' linear programming problem.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, May 1992.

\bibitem{ipm:Freund28}
R.~M. Freund.
\newblock Projective transformations for interior--point algorithms, and a
  superlinearly convergent algorithm for the w--center problem.
\newblock {\em Mathematical Programming}, 58:385--414, 1993.
\newblock Amalgamation of Freund \cite{ipm:Freund5,ipm:Freund6}.

\bibitem{ipm:Freund30}
R.~M. Freund.
\newblock Complexity of an algorithm for finding an approximate solution of a
  semi--definite program, with no regularity condition.
\newblock {Working Paper} OR--302--94, Operations Research Center,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, 1994.

\bibitem{ipm:Freund20}
R.~M. Freund.
\newblock A potential reduction algorithm with user--specified
  {phase\,I\,---\,phase\,II} balance for solving a linear program from an
  infeasible warm start.
\newblock {\em SIAM Journal on Optimization}, 5:247--268, 1995.

\bibitem{ipm:Freund29}
R.~M. Freund.
\newblock An infeasible--start algorithm for linear programming whose
  complexity depends on the distance from the starting point to the optimal
  solution.
\newblock {\em Annals of Operations Research}, 62:29--57, 1996.

\bibitem{ipm:Freund35}
R.~M. Freund and S.~Mizuno.
\newblock Interior point methods\,: {Current} status and future directions.
\newblock {\em Optima (The Mathematical Programming Society Newsletter)},
  51:1--9, 1996.

\bibitem{ipm:Freund33}
R.~M. Freund and M.~A. Nunez.
\newblock Condition measures and properties of the central trajectory of a
  linear program.
\newblock {Sloan Working Paper}, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, March 1996.
\newblock Submitted to {\em Mathematical Programming}. Identical version to
  Nunez and Freund \cite{ipm:Nunez2}.

\bibitem{ipm:Freund14}
R.~M. Freund and K.~C. Tan.
\newblock A parametric center algorithm and a strictly monotonic central path
  algorithm for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Sloan School of Management, Massachusetts Institute of Technology,
  Cambridge, MA~02139, USA, October 1989.

\bibitem{ipm:Freund15}
R.~M. Freund and K.~C. Tan.
\newblock Newton's method for parametric center problems.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, Sloan
  School of Management, Massachusetts Institute of Technology, Cambridge,
  MA~02139, USA, July 1990.

\bibitem{ipm:Freund21}
R.~M. Freund and K.~C. Tan.
\newblock Newton's method for the general parametric centering problem with
  applications.
\newblock {Working Paper}, Sloan School of Management, Massachusetts Institute
  of Technology, Cambridge, MA~02139, USA, 1990.
\newblock To appear in {\em Mathematical Programming}.

\bibitem{ipm:Freund13}
R.~M. Freund and K.~C. Tan.
\newblock A method for the parametric center problem, with a strictly monotone
  polynomial--time algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):775--801, 1991.

\bibitem{ipm:Freund27}
R.~M. Freund and M.~J. Todd.
\newblock Barrier functions and interior--point algorithms for linear
  programming with zero--, one--, or two--sided bounds of the variables.
\newblock {\em Mathematics of Operations Research}, 20:415--440, 1995.

\bibitem{ipm:Freund36}
R.~M. Freund and J.~Vera.
\newblock Condition--based complexity of convex optimization in conic linear
  form via the ellipsoid algorithm.
\newblock {Technical Report}, Operations Research Center, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, September 1997.

\bibitem{ipm:Freund32}
R.~M. Freund and J.~R. Vera.
\newblock Some characterizations and properties of the distance to
  ill--posedness and the condition measure of a conic linear system.
\newblock {Sloan Working Paper} 3862--95--MSA, Sloan School of Management,
  Massachusetts Institute of Technology, Cambridge, MA~02139, USA, November
  1995.
\newblock Submitted to {\em Mathematical Programming}.

\bibitem{ipm:Freund31}
R.~M. Freund and H.~K. Wadhwa.
\newblock Implementation and empirical study of a combined
  {phase\,I\,--\,phase\,II} potential reduction algorithm for linear
  programming.
\newblock {Working Paper} 3411--92, Sloan School of Management, Massachusetts
  Institute of Technology, Cambridge, MA~02139, USA, March 1992.

\bibitem{ipm:RFreund1}
R.~W. Freund and F.~Jarre.
\newblock An interior--point method for convex fractional programming.
\newblock {AT \& T Numerical Analysis Manuscript} 93--03, AT{\&}T Bell
  Laboratories, Murray Hill, NJ~07974, USA, May 1993.

\bibitem{ipm:RFreund3}
R.~W. Freund and F.~Jarre.
\newblock On the complexity of convex fractional programs.
\newblock {Technical Report (in preparation)}, AT{\&}T Bell Laboratories,
  Murray Hill, NJ~07974, USA, 1993.

\bibitem{ipm:RFreund4}
R.~W. Freund and F.~Jarre.
\newblock An interior--point method for fractional programs with convex
  constraints.
\newblock {\em Mathematical Programming}, pages 407--440, 1994.
\newblock See also {\em Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik
  74(1994), T523--T525}.

\bibitem{ipm:RFreund2}
R.~W. Freund and F.~Jarre.
\newblock An interior--point method for multi--fractional programming with
  convex constraints.
\newblock {\em Journal of Optimization Theory and Applications}, 85:125--161,
  1995.

\bibitem{ipm:RFreund6}
R.~W. Freund and F.~Jarre.
\newblock A {QMR}--based interior--point algorithm for solving linear programs.
\newblock {\em Mathematical Programming}, 76:183--210, 1997.

\bibitem{ipm:RFreund8}
R.~W. Freund, F.~Jarre, and S.~Mizuno.
\newblock Convergence of a class of inexact interior--point algorithms for
  linear program.
\newblock {Numerical Analysis Manuscript} 97--3--11, AT{\&}T Bell Laboratories,
  Murray Hill, NJ~07974, USA, October 1997.

\bibitem{ipm:RFreund5}
R.~W. Freund, F.~Jarre, and S.~Schaible.
\newblock On interior--point methods for fractional programs and their convex
  reformulation.
\newblock {AT \& T Numerical Analysis Manuscript} 94--17, AT{\&}T Bell
  Laboratories, Murray Hill, NJ~07974, USA, 1994.

\bibitem{ipm:RFreund7}
R.~W. Freund, F.~Jarre, and S.~Schaible.
\newblock On self--concordant barrier functions for conic hulls and fractional
  programming.
\newblock {\em Mathematical Programming}, 74:237--246, 1996.

\bibitem{ipm:Fricker1}
F.~Fricker.
\newblock {Komplexe Optimierungsaufgaben schneller l{\"o}sen~(Solving complex
  optimization problems faster)}.
\newblock {\em Frankfurter Allgemeine Zeitung, Sektion\,: Natur und Wissen},
  March 27, 1985.
\newblock (In German).

\bibitem{ipm:Frisch3}
K.~R. Frisch.
\newblock Principles of linear programming---{With} a particular reference to
  the double gradient form of the logarithmic potential method.
\newblock Memorandum, Institute of Economics, University of Oslo, Oslo, Norway,
  October 1954.

\bibitem{ipm:Frisch5}
K.~R. Frisch.
\newblock Principles of linear programming--the double gradient form of the
  logarithmic potential method.
\newblock Memorandum, Institute of Economics, University of Oslo, Oslo, Norway,
  October 1954.

\bibitem{ipm:Frisch1}
K.~R. Frisch.
\newblock The logarithmic potential method for convex programming.
\newblock Unpublished manuscript, Institute of Economics, University of Oslo,
  Oslo, Norway, May 1955.

\bibitem{ipm:Frisch6}
K.~R. Frisch.
\newblock La resolution des problemes de programme lineaire par la methode du
  potential logarithmique.
\newblock {\em Cahiers du Seminaire D'Econometrie}, 4:7--20, 1956.

\bibitem{ipm:Frisch4}
K.~R. Frisch.
\newblock Linear dependencies and a mechanized form of the multiplex method for
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\newblock Memorandum, Institute of Economics, University of Oslo, Oslo, Norway,
  1957.

\bibitem{ipm:Frisch2}
K.~R. Frisch.
\newblock The multiplex method for linear programming.
\newblock {\em Sankhya}, 18:329--362, 1957.

\bibitem{ipm:Fu1}
M.~Fu, Z.-Q. Luo, and Y.~Ye.
\newblock Approximation algorithms for quadratic programming.
\newblock {\em Journal of Combinatorial Optimization}, 2:29--50, 1998.

\bibitem{ipm:Fujie1}
T.~Fujie and M.~Kojima.
\newblock Semidefinite programming relaxation for nonconvex quadratic programs.
\newblock {\em Journal of Global Optimization}, 10:367--380, 1997.

\bibitem{ipm:Fujisawa5}
K.~Fujisawa.
\newblock Numerical experiments on interior point method programs related to
  positive semidefinite programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
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\newblock (In Japanese, English summary).

\bibitem{ipm:Fujisawa4}
K.~Fujisawa, M.~Fukuda, M.~Kojima, and K.~Nakata.
\newblock Numerical evaluation of {SDPA (SemiDefinite Programming Algorithm)}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
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  September 1997.

\bibitem{ipm:Fujisawa2}
K.~Fujisawa and M.~Kojima.
\newblock {SDPA (Semi--Definite Programming Algorithm) --- The Software}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research}, Department of Information Sciences, Tokyo Institute of Technology,
  Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, November 1995.

\bibitem{ipm:Fujisawa1}
K.~Fujisawa and M.~Kojima.
\newblock {SDPA (Semi--Definite Programming Algorithm) --- User's Manual}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--308, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, November 1995.
\newblock Revised August 1996.

\bibitem{ipm:Fujisawa3}
K.~Fujisawa, M.~Kojima, and K.~Nakata.
\newblock Exploiting sparsity in primal--dual interior--point methods for
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\newblock {\em Mathematical Programming}, 78:235--253, 1997.

\bibitem{ipm:Fukushima1}
M.~Fukushima, N.~Arai, and T.~Ibaraki.
\newblock An interior method for nonlinear minimum cost network flow problems.
\newblock {\em Systems and Control (Japan)}, 31(11):837--843, 1987.

\bibitem{ipm:Gahinet1}
P.~Gahinet and A.~S. Nemirovsky.
\newblock The projective method for solving linear matrix inequalities.
\newblock {\em Mathematical Programming}, 77:163--190, 1997.
\newblock See also Nemirovsky and Gahinet \cite{ipm:Nemirovsky5}.

\bibitem{ipm:Garcia1}
C.~B. Garcia and F.~J. Gould.
\newblock An application of homotopy to solving linear programs.
\newblock {\em Mathematical Programming}, 27:263--282, 1983.

\bibitem{ipm:Garey1}
M.~R. Garey and D.~M. Gay.
\newblock Letter from the {AT~\&~T Laboratories}.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
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\bibitem{ipm:Garfunkel1}
S.~A. Garfunkel, L.~A. Steen, and J.~Malkevitch.
\newblock {\em For All Practical Purposes\,: Introduction to Contemporary
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  simplex method, pages 80--83, 362.
\newblock W. H. Freeman and Company, New York, 1988.

\bibitem{ipm:Garzillo1}
A.~Garzillo, M.~Innorta, and M.~Ricci.
\newblock The problem of active and reactive optimum power dispatching solving
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\newblock {\em Energia Elettrica}, 74:113--122, 1997.

\bibitem{ipm:Gassmann1}
H.~I. Gassmann.
\newblock Interior point methods in stochastic linear programming\,: {Reducing}
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\newblock {Working Paper} WP--91--4, Dalhousie School of Business
  Administration, Dalhousie University, Halifax, Canada~B3H\,1Z5, 1991.
\newblock Available through\,: http://ttg.sba.dal.ca/sba/doc/fillin.ps or
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D.~M. Gay.
\newblock Sparse projections in {Karmarkar's} linear programming algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Atlanta, GA,
  USA}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, November 1985.
\newblock No underlying report.

\bibitem{ipm:Gay2}
D.~M. Gay.
\newblock Pictures of {Karmarkar's} linear programming algorithm.
\newblock {Computer Science Technical Report} 136, AT~\&~T~Bell Laboratories,
  Murray Hill, NJ~07974, USA, January 1987.

\bibitem{ipm:Gay3}
D.~M. Gay.
\newblock A variant of {Karmarkar's} linear programming algorithm for problems
  in standard form.
\newblock {\em Mathematical Programming}, 37:81--90, 1987.
\newblock Errata in {\em Mathematical Programming}, 40:111, 1988.

\bibitem{ipm:Gay4}
D.~M. Gay.
\newblock Massive memory buys little speed for complete, in--core sparse
  {C}holesky factorizations on some scalar computers.
\newblock {\em Linear Algebra and Its Applications}, 152:291--314, 1991.

\bibitem{ipm:Gay5}
D.~M. Gay.
\newblock Stopping tests that compute optimal solutions for interior--point
  linear programming algorithms.
\newblock In S.~Gomez, J.~P. Hennart, and R.~A. Tapia, editors, {\em Advances
  in Numerical Partial Differential Equations and Optimization\,: Proceedings
  of the Fifth Mexico--United States Workshop}, volume~47 of {\em Proceedings
  in Applied Mathematics}, pages 17--42. SIAM Publications, Philadelphia, PA,
  USA, 1991.

\bibitem{ipm:Gay6}
D.~M. Gay, N.~K. Karmarkar, and K.~G. Ramakrishnan.
\newblock The {Karmarkar} algorithm\,: {Adding} wings to linear programming.
\newblock {\em Record AT~\&~T~Bell Laboratories}, 64(2):4--10, 1986.

\bibitem{ipm:Gay7}
D.~M. Gay, M.~Kojima, and R.~A. Tapia.
\newblock {\em Interior Point Methods for Linear Programming}, volume 152 of
  {\em Linear Algebra and Its Applications}.
\newblock North Holland, Amsterdam, The Netherlands, July 1991.
\newblock (Special issue).

\bibitem{ipm:Gay8}
D.~M. Gay, M.~L. Overton, and M.~H. Wright.
\newblock Primal--dual interior point methods for indefinite nonlinear
  programming.
\newblock {Technical Report}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974,
  USA, 1995.
\newblock (In preparation).

\bibitem{ipm:Gay9}
D.~M. Gay, M.~L. Overton, and M.~H. Wright.
\newblock A primal--dual interior point method for nonconvex nonlinear
  programming.
\newblock {Technical Report} 97--4--08, AT~\&~T~Bell Laboratories, Murray Hill,
  NJ~07974, USA, July 1997.
\newblock To appear in {\em{Advances in Nonlinear Programming, Y. Yuan (ed.),
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998}}.

\bibitem{ipm:Ge1}
R.~Ge.
\newblock Solving linear programming problems via linear minimax problems.
\newblock {\em Applied Mathematics and Computation}, 46(1):59--77, 1991.

\bibitem{ipm:Gelbaum1}
B.~R. Gelbaum.
\newblock {\em Linear Algebra\,: Basics, Practice and Theory}, chapter 5.7~:
  {The Karmarkar algorithm}, pages 504--527.
\newblock North Holland, New York, 1989.

\bibitem{ipm:Ghare1}
P.~Ghare.
\newblock Free decision variables and simplified interior point methods for
  linear programming.
\newblock {Talk held at the Symposium APMOD\,'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Northern Virginia Graduate Centre, USA, January 1991.

\bibitem{ipm:Ghellinck1}
{G. de} Ghellinck and J.-Ph. Vial.
\newblock A polynomial {N}ewton method for linear programming.
\newblock {\em Algorithmica}, 1(4):425--453, 1986.

\bibitem{ipm:Ghellinck2}
{G. de} Ghellinck and J.-Ph. Vial.
\newblock An extension of {Karmarkar's} algorithm for solving a system of
  linear homogeneous equations on the simplex.
\newblock {\em Mathematical Programming}, 39:79--92, 1987.

\bibitem{ipm:Ghellinck3}
{G. de} Ghellinck and J.-Ph. Vial.
\newblock A unified approach to projective and affine algorithms for linear
  programming.
\newblock {Talk held at the EURO/TIMS Joint International Conference on
  Operational Research in Paris, France}, Center of Operations Research and
  Econometrics, Universite Catholique de Louvain, B--1348~Louvain--la--Neuve,
  Belgium, July 1988.

\bibitem{ipm:Gill6}
P.~E. Gill, A.~Marxen, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock Solution of the primal {LP}-problem by a barrier method\,: {S}ome
  implementation aspects.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Systems Optimization Laboratory, Department of Operations Research,
  Stanford University, Stanford, CA~94305, USA, April 1988.
\newblock See Marxen \cite{ipm:Marxen1,ipm:Marxen2}.

\bibitem{ipm:Gill9}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Solving reduced {KKT}--systems in barrier methods for linear and
  quadratic programming.
\newblock {Technical Report} SOL~91-7, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, July 1991.
\newblock See also Gill et al. \cite{ipm:Gill12}.

\bibitem{ipm:Gill11}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Preconditioners for indefinite systems arising in optimization.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 13:292--311,
  1992.

\bibitem{ipm:Gill12}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Solving reduced {KKT}--systems in barrier methods for linear
  programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
  1993}, volume 303 of {\em Pitman Research Notes in Mathematics}, pages
  89--104. Longman Scientific \& Technical, Harlow, United Kingdom, 1994.
\newblock See also Gill et al. \cite{ipm:Gill9}.

\bibitem{ipm:Gill8}
P.~E. Gill, W.~Murray, D.~B. Poncele{\'o}n, and M.~A. Saunders.
\newblock Primal--dual methods for linear programming.
\newblock {\em Mathematical Programming}, 70:251--277, 1995.

\bibitem{ipm:Gill2}
P.~E. Gill, W.~Murray, and M.~A. Saunders.
\newblock Interior--point methods for linear programs\,: {A} challenge to the
  simplex method.
\newblock {Technical Report} SOL~88--14, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, July 1988.

\bibitem{ipm:Gill1}
P.~E. Gill, W.~Murray, and M.~A. Saunders.
\newblock A single\,--\,phase dual barrier method for linear programming.
\newblock {Technical Report} SOL~88--10, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, August 1988.

\bibitem{ipm:Gill7}
P.~E. Gill, W.~Murray, M.~A. Saunders, J.~A. Tomlin, and M.~H. Wright.
\newblock On projected {Newton} barrier methods for linear programming and an
  equivalence to {Karmarkar's} projective method.
\newblock {\em Mathematical Programming}, 36:183--209, 1986.

\bibitem{ipm:Gill3}
P.~E. Gill, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock A note on nonlinear approaches to linear programming.
\newblock {Technical Report} SOL~86--7, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, April 1986.

\bibitem{ipm:Gill4}
P.~E. Gill, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock Convergence results for a shifted barrier linear programming method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Systems Optimization Laboratory, Department of Operations Research,
  Stanford University, Stanford, CA~94305, USA, April 1988.

\bibitem{ipm:Gill5}
P.~E. Gill, W.~Murray, M.~A. Saunders, and M.~H. Wright.
\newblock Shifted barrier methods for linear programming.
\newblock {Technical Report} SOL~88--9, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, August 1988.

\bibitem{ipm:Gill10}
P.~E. Gill, W.~Murray, and M.~H. Wright.
\newblock {\em Numerical Linear Algebra and Optimization, {V}ol.\,2}.
\newblock Addison Wesley Publishing Company, Amsterdam, The Netherlands, 1992.
\newblock Chapter on interior point methods.

\bibitem{ipm:Gill13}
P.~E. Gill, M.~A. Saunders, and J.~R. Shinnerl.
\newblock On the stability of {Cholesky} factorization for symmetric
  quasidefinite systems.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 17:35--46,
  1996.

\bibitem{ipm:Glassman1}
N.~D. Glassman.
\newblock {ONR (Office of Naval Research)} focuses on interior methods.
\newblock {\em SIAM News}, 20(2):12, March 1987.

\bibitem{ipm:Gleick1}
J.~Gleick.
\newblock Breakthrough in problem solving.
\newblock {\em The New York Times}, November 19, 1984.

\bibitem{ipm:Goessl1}
H.~Goessl.
\newblock {Eine Modifikation des Verfahrens von Karmarkar basierend auf einer
  Formulierung des Algorithmus im Originalproblem~(A modification of
  Karmarkar's algorithm based on a formulation of the algorithm in the original
  problem)}.
\newblock {Interner Bericht der intergrierten Arbeitsgruppe Mathematische
  Probleme aus dem Ingenieurbereich}, Fachbereich Mathematik, Gesamthochschule
  Wuppertal, D--42097~Wuppertal~1, Germany, October 1986.
\newblock (In German).

\bibitem{ipm:Goessl2}
H.~Goessl.
\newblock {Eine Verallgemeinerung und eine duale Variante des Verfahrens von de
  Ghellinck und Vial zur linearen Optimierung~(A generalization and a dual
  variant of the algorithm of de Ghellinck and Vial for linear programming)}.
\newblock {Interner Bericht der intergrierten Arbeitsgruppe Mathematische
  Probleme aus dem Ingenieurbereich}, Fachbereich Mathematik, Gesamthochschule
  Wuppertal, D--42097~Wuppertal~1, Germany, December 1987.
\newblock (In German).

\bibitem{ipm:Goessl3}
H.~Goessl.
\newblock {\em {Varianten der polynomialen Newtonmethode zur linearen
  Optimierung~(Variants of the polynomial Newton method for linear
  programming)}}.
\newblock PhD thesis, Fachbereich Mathematik, Gesamthochschule Wuppertal,
  D--42097~Wuppertal~1, Germany, 1989.
\newblock (In German).

\bibitem{ipm:Goffin8}
J.-L. Goffin.
\newblock Affine methods in nondifferentiable optimization.
\newblock {CORE Discussion Paper} 8744, Center for Operations Research and
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  Belgium, 1987.

\bibitem{ipm:Goffin1}
J.-L. Goffin.
\newblock Affine and projective methods in nondifferentiable optimization.
\newblock In K.~H. Hoffmann, J.~B. Hiriat-Urruty, C.~Lemarechal, and J.~Zowe,
  editors, {\em Trends in Mathematical Optimization\,: Proceedings of the 4th
  French--German Conference on Optimization in Irsee, Germany, April 1986},
  volume~84 of {\em International Series of Numerical Mathematics}, pages
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\bibitem{ipm:Goffin2}
J.-L. Goffin.
\newblock Decomposition and large scale optimization with the interior point
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Faculty of Management, McGill University, Montreal, Ontario,
  Canada, October 1990.

\bibitem{ipm:Goffin16}
J.-L. Goffin.
\newblock Using the primal dual infeasible {Newton} method in the analytic
  center method for problems defined by deep cutting planes.
\newblock {Technical Report}, Faculty of Management, McGill University,
  Montreal, Ontario, Canada, September 1994.

\bibitem{ipm:Goffin13}
J.-L. Goffin, J.~Gondzio, R.~Sarkissian, and J.-Ph. Vial.
\newblock Solving nonlinear multicommodity flow problems by the analytic center
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\newblock {\em Mathematical Programming}, 76:131--154, 1997.

\bibitem{ipm:Goffin4}
J.-L. Goffin, A.~Haurie, and J.-Ph. Vial.
\newblock Decomposition and nondifferentiable optimization with the projective
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\newblock {\em Management Science}, 38(2):284--302, 1992.

\bibitem{ipm:Goffin7}
J.-L. Goffin, A.~Haurie, J.-Ph. Vial, and D.~L. Zhu.
\newblock Using central prices in the decomposition of linear programs.
\newblock {\em European Journal of Operational Research}, 64:393--409, 1993.

\bibitem{ipm:Goffin15}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock Further complexity analysis of a primal--dual column generation
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\newblock {Technical Report}, Faculty of Management, McGill University,
  Montreal, Ontario, Canada, August 1993.
\newblock To appear in {\em SIAM Journal on Optimization}.

\bibitem{ipm:Goffin14}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock Complexity analysis of a potential reduction and column generation
  algorithm for convex programming.
\newblock {Technical Report}, Faculty of Management, McGill University,
  Montreal, Ontario, Canada, 1994.
\newblock To appear in {\em SIAM Journal on Optimization}.

\bibitem{ipm:Goffin11}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock On the complexity of a column generation algorithm for convex or
  quasiconvex feasibility problems.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
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\bibitem{ipm:Goffin12}
J.-L. Goffin, Z.-Q. Luo, and Y.~Ye.
\newblock Complexity analysis of an interior cutting plane method for convex
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\newblock {\em SIAM Journal on Optimization}, 6:638--652, 1996.

\bibitem{ipm:Goffin17}
J.-L. Goffin, P.~Marcotte, and D.~Zhu.
\newblock An analytic center cutting plane method for pseudomonotone
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\newblock {\em Operations Research Letters}, 20:1--6, 1997.

\bibitem{ipm:Goffin18}
J.-L. Goffin and F.~Sharifi-Mokhtarian-Mokhtarian.
\newblock Using the primal dual infeasible {Newton} method in the analytic
  center method for problems defined by deep cutting planes.
\newblock {Technical Report} GERAD G--94--41, Faculty of Management, McGill
  University, Montreal, Ontario, Canada, 1994.
\newblock Revised April 1996.

\bibitem{ipm:Goffin10}
J.-L. Goffin and J.-Ph. Vial.
\newblock On the computation of weighted analytic centers and dual ellipsoids
  with the projective algorithm.
\newblock {Manuscript}, Faculte des Sciences Economiques et Sociales,
  Universite de Geneve, Geneve, Suisse, July 1989.

\bibitem{ipm:Goffin3}
J.-L. Goffin and J.-Ph. Vial.
\newblock Cutting planes and column generation techniques with the projective
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\newblock {\em Journal of Optimization Theory and Applications}, 65:409--429,
  1990.

\bibitem{ipm:Goffin9}
J.-L. Goffin and J.-Ph. Vial.
\newblock Experimentation with the interior cutting plane method {(ICPM)}.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Faculty of Management, McGill University, Montreal, Ontario,
  Canada, May 1992.

\bibitem{ipm:Goffin6}
J.-L. Goffin and J.-Ph. Vial.
\newblock On the computation of weighted analytic centers and dual ellipsoids
  with the projective algorithm.
\newblock {\em Mathematical Programming}, 60:81--92, 1993.

\bibitem{ipm:Goffin5}
J.-L. Goffin and J.-Ph. Vial.
\newblock Short steps with {Karmarkar's} projective algorithm for linear
  programming.
\newblock {\em SIAM Journal on Optimization}, 4:193--207, 1994.

\bibitem{ipm:Goffin20}
J.-L. Goffin and J.-Ph. Vial.
\newblock A two--cut approach in the analytic center cutting plane method.
\newblock {Logilab Technical Report} 97.6, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva, Switzerland,
  August 1997.

\bibitem{ipm:Goffin21}
J.-L. Goffin and J.-Ph. Vial.
\newblock Multiple cuts in the analytic center cutting plane method.
\newblock {Logilab Technical Report} 98.10, LOGILAB, HEC Geneva, Department of
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  Switzerland, June 1998.

\bibitem{ipm:Goffin19}
J.-L. Goffin and J.-Ph. Vial.
\newblock Shallow, deep and very deep cuts in the analytic center cutting plane
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\newblock {\em Mathematical Programming}, 84:89--103, 1999.

\bibitem{ipm:Goldberg1}
A.~V. Goldberg, S.~A. Plotkin, D.~B. Shmoys, and E.~Tardos.
\newblock Interior--point methods in parallel computation.
\newblock In {\em Proceedings of the 30th Annual Symposium on Foundations of
  Computer Science, Research Triangle Park, NC, USA, 1989}, pages 350--355.
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\bibitem{ipm:Goldberg2}
A.~V. Goldberg, S.~A Plotkin, D.~B. Shmoys, and E.~Tardos.
\newblock Using interior--point methods for fast parallel algorithms for
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\newblock {\em SIAM Journal on Computing}, 21(1):140--150, 1992.

\bibitem{ipm:Goldfarb1}
D.~Goldfarb.
\newblock A relaxed version of {Karmarkar's} method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
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\bibitem{ipm:Goldfarb2}
D.~Goldfarb.
\newblock A primal projective interior point method for linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
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\bibitem{ipm:Goldfarb10}
D.~Goldfarb and S.~Liu.
\newblock Interior point potential function reduction algorithm for solving
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\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, 1990.

\bibitem{ipm:Goldfarb3}
D.~Goldfarb and S.~Liu.
\newblock An ${O(n^{3}L)}$ primal interior point algorithm for convex quadratic
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\newblock {\em Mathematical Programming}, 49:325--340, 1990/91.

\bibitem{ipm:Goldfarb12}
D.~Goldfarb and S.~Liu.
\newblock An {$O(n^{3}L)$} primal--dual potential reduction algorithm for
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\newblock {\em Mathematical Programming}, 61:161--170, 1993.

\bibitem{ipm:Goldfarb9}
D.~Goldfarb, S.~Liu, and S.~Wang.
\newblock A logarithmic barrier function algorithm for quadratically
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\newblock {\em SIAM Journal on Optimization}, 1:252--267, 1991.

\bibitem{ipm:Goldfarb6}
D.~Goldfarb and S.~Mehrotra.
\newblock A homogeneous equations variant of {Karmarkar's} algorithm for
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\newblock {Talk held at ORSA/TIMS Joint National Meeting in New Orleans, USA},
  Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, May 1987.

\bibitem{ipm:Goldfarb5}
D.~Goldfarb and S.~Mehrotra.
\newblock Relaxed variants of {Karmarkar's} algorithm for linear programs with
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\newblock {\em Mathematical Programming}, 40:183--195, 1988.

\bibitem{ipm:Goldfarb4}
D.~Goldfarb and S.~Mehrotra.
\newblock A relaxed version of {Karmarkar's} method.
\newblock {\em Mathematical Programming}, 40:289--315, 1988.

\bibitem{ipm:Goldfarb7}
D.~Goldfarb and S.~Mehrotra.
\newblock A self--correcting version of {Karmarkar's} algorithm.
\newblock {\em SIAM Journal on Numerical Analysis}, 26:1006--1015, 1989.

\bibitem{ipm:Goldfarb15}
D.~Goldfarb and K.~Scheinberg.
\newblock Interior point trajectories in semidefinite programs.
\newblock {\em SIAM Journal on Optimization}, 8:871--886, 1998.

\bibitem{ipm:Goldfarb13}
D.~Goldfarb and D.~X. Shaw.
\newblock A path--following projective interior point method for linear
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\newblock {Technical Report}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, 1991.
\newblock To appear in {\em SIAM Journal on Optimization}.

\bibitem{ipm:Goldfarb14}
D.~Goldfarb and D.~X. Shaw.
\newblock On the complexity of a class of projective interior point methods.
\newblock {\em Mathematics of Operations Research}, 20:116--134, 1995.

\bibitem{ipm:Goldfarb8}
D.~Goldfarb and M.~J. Todd.
\newblock {Linear Programming}.
\newblock In G.~L. Nemhauser, A.~H.~G. {Rinnooy Kan}, and M.~J. Todd, editors,
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\bibitem{ipm:Goldfarb11}
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\newblock A primal projective interior point method for linear programming.
\newblock {\em Mathematical Programming}, 51:17--43, 1991.

\bibitem{ipm:Golshtejn1}
E.~G. Gol'shtejn, A.~S. Nemirovsky, and Yu.~E. Nesterov.
\newblock On some recent advances in optimization.
\newblock {\em Ekonomika i Matematickeskie Metody (Moscow)}, 26(1):178--190,
  1990.
\newblock (In Russian).

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J.~Gondzio.
\newblock An advanced implementation of {Cholesky} factorization for computing
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\newblock Cahier 107, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, December 1991.
\newblock Published in Gondzio\,\cite{ipm:Gondzio4} after title change.

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J.~Gondzio.
\newblock Splitting dense columns of constraint matrix in interior point
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\newblock {\em Optimization}, 24:285--297, 1992.

\bibitem{ipm:Gondzio4}
J.~Gondzio.
\newblock Implementing {Cholesky} factorization for interior point methods of
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\newblock {\em Optimization}, 27:121--140, 1993.
\newblock Title change version of Gondzio\,\cite{ipm:Gondzio2}.

\bibitem{ipm:Gondzio11}
J.~Gondzio.
\newblock Preconditioned conjugate gradients in an interior point method for
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\newblock {Working Paper} WP--94--130, IIASA International Institute for
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J.~Gondzio.
\newblock {HOPDM (Version2.12) -- A fast LP} solver based on a primal--dual
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\newblock {\em European Journal of Operational Research}, 85:221--225, 1995.
\newblock See also Altman and Gondzio \cite{ipm:Altman3}.

\bibitem{ipm:Gondzio10}
J.~Gondzio.
\newblock On the use of multiple centrality corrections in a primal--dual
  method for large scale linear programming.
\newblock {\em International Symposium of Economic Informatics (Bucharest,
  Romania, May 1995)}, pages 311--321, 1995.
\newblock See also Gondzio \cite{ipm:Gondzio8}.

\bibitem{ipm:Gondzio8}
J.~Gondzio.
\newblock Multiple centrality corrections in a primal--dual method for linear
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\newblock {\em Computational Optimization and Applications}, 6:137--156, 1996.
\newblock See also Gondzio \cite{ipm:Gondzio10}.

\bibitem{ipm:Gondzio5}
J.~Gondzio.
\newblock Presolve analysis of linear programs prior to applying the
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\newblock {\em INFORMS Journal on Computing}, 9:73--91, 1997.

\bibitem{ipm:Gondzio17}
J.~Gondzio.
\newblock Warm start of the priml--dual method applied in the cutting plane
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\newblock {\em Mathematical Programming}, 83:125--143, 1998.

\bibitem{ipm:Gondzio12}
J.~Gondzio and M.~Makowski.
\newblock {HOPDM--Modular solver for LP problems user's guide to version\,
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\newblock {Working Paper} WP--95--50, IIASA International Institute for Applied
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\bibitem{ipm:Gondzio6}
J.~Gondzio and M.~Makowski.
\newblock Solving a class of {LP} problems with a primal--dual logarithmic
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\newblock {\em European Journal of Operational Research}, 80:184--192, 1995.

\bibitem{ipm:Gondzio13}
J.~Gondzio and {O. du} Merle.
\newblock Analytic center cutting plane method -- {User's} guide for the
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\newblock {Technical Report} 1995.33, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, December 1995.

\bibitem{ipm:Gondzio14}
J.~Gondzio, {O. du} Merle, R.~Sarkissian, and J.-Ph. Vial.
\newblock {ACCPM} -- a library for convex optimization based on an analytic
  center cutting plane method.
\newblock {Technical Report} 1995.34, Department of Management Studies,
  University of Geneva, CH--1211 Geneva, Switzerland, December 1995.

\bibitem{ipm:Gondzio16}
J.~Gondzio and R.~Sarkissian.
\newblock Column generation with a primal--dual method.
\newblock {Logilab Technical Report} 96.6, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva, Switzerland, June
  1996.

\bibitem{ipm:Gondzio15}
J.~Gondzio, R.~Sarkissian, and J.-Ph. Vial.
\newblock Using an interior point method for the master problems in a
  decomposition approach.
\newblock {\em European Journal of Operational Research}, 101:577--587, 1997.

\bibitem{ipm:Gondzio19}
J.~Gondzio, R.~Sarkissian, and J.-Ph. Vial.
\newblock Parallel implementation of a central decomposition method for solving
  large scale planning problems.
\newblock {Logilab Technical Report} 98.1, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva~4, Switzerland,
  January 1998.

\bibitem{ipm:Gondzio3}
J.~Gondzio and D.~Tachat.
\newblock The design and application of the {IMPLO -- A FORTRAN} library for
  linear optimization with interior point methods.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  28:37--56, 1994.

\bibitem{ipm:Gondzio7}
J.~Gondzio and T.~Terlaky.
\newblock A computational view of interior point methods.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
  Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
  Applications}, pages 103--144. Oxford Science Publications, Oxford University
  Press, Oxford, Great Britain, 1996.

\bibitem{ipm:Gondzio18}
J.~Gondzio and J.-Ph. Vial.
\newblock Warm start and epsilon--subgradients in the cutting plane scheme for
  block--angular linear programs.
\newblock {Logilab Technical Report} 97.1, LOGILAB, HEC Geneva, Department of
  Management Studies, University of Geneva, CH--1211 Geneva~4, Switzerland,
  June 1997.

\bibitem{ipm:Gong1}
D.~P. Gong and S.~R. Xu.
\newblock An interior point algorithm for solving linear programming problems
  with hybrid constraints.
\newblock {\em Sinica Naturalis Univ.\,Sunyatsemi}, 31(4):19--25, 1992.
\newblock (In Chinese, English summary).

\bibitem{ipm:Gonzaga28}
C.~C. Gonzaga.
\newblock {\em {Interior--Point Algorithms}}.
\newblock Brooks\,\&\,Cole Publishing Company, Pacific Grove, CA, USA.
\newblock (In preparation).

\bibitem{ipm:Gonzaga13}
C.~C. Gonzaga.
\newblock A conical projection algorithm for linear programming.
\newblock Memorandum UCB/ERL~M85/61, Electronics Research Laboratory,
  University of California, Berkeley, CA~94720, USA, July 1985.

\bibitem{ipm:Gonzaga1}
C.~C. Gonzaga.
\newblock New results in conical projection methods for mathematical
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
  FL, USA}, Department of Electrical Engineering and Computer Science,
  University of California, Berkeley, CA~94720, USA, October 1986.

\bibitem{ipm:Gonzaga17}
C.~C. Gonzaga.
\newblock Trust region minimization in conical projection algorithms.
\newblock {Talk held at the Eleventh IFORS International Conference on
  Operations Research in Buenos Aires, Argentina}, Department of Electrical
  Engineering and Computer Science, University of California, Berkeley,
  CA~94720, USA, August 1987.

\bibitem{ipm:Gonzaga15}
C.~C. Gonzaga.
\newblock A simple representation of {Karmarkar's} algorithm.
\newblock {Technical Report}, Department of Systems Engineering and Computer
  Science, COPPE Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro,
  RJ, Brazil, May 1988.

\bibitem{ipm:Gonzaga6}
C.~C. Gonzaga.
\newblock An algorithm for solving linear programming problems in ${O(n^{3}L)}$
  operations.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 1--28. Springer Verlag, New York,
  1989.

\bibitem{ipm:Gonzaga5}
C.~C. Gonzaga.
\newblock Conical projection algorithms for linear programming.
\newblock {\em Mathematical Programming}, 43:151--173, 1989.

\bibitem{ipm:Gonzaga20}
C.~C. Gonzaga.
\newblock Path--following algorithms for linear and quadratic programming.
\newblock {Talk held at the Third SIAM Conference on Optimization in Boston,
  MA, USA}, Department of Systems Engineering and Computer Science, COPPE
  Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil, April
  1989.

\bibitem{ipm:Gonzaga18}
C.~C. Gonzaga.
\newblock Convergence of the large step primal affine--scaling algorithm for
  primal nondegenerate linear programs.
\newblock {Technical Report} ES--230/90, Department of Systems Engineering and
  Computer Science, COPPE Federal University of Rio de Janeiro,
  21941~Rio~de~Janeiro, RJ, Brazil, September 1990.

\bibitem{ipm:Gonzaga11}
C.~C. Gonzaga.
\newblock Large steps potential reduction algorithms for linear programming.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Department of Systems Engineering and Computer Science, COPPE Federal
  University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil, July 1990.

\bibitem{ipm:Gonzaga10}
C.~C. Gonzaga.
\newblock A larger step path--following potential reduction algorithm for
  linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Department of Systems Engineering and Computer Science, COPPE
  Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil,
  January 1990.

\bibitem{ipm:Gonzaga9}
C.~C. Gonzaga.
\newblock An overview of ${O(\sqrt{n}L)}$--iteration algorithms for linear
  programming.
\newblock {Talk held at the 14th Conference on the Mathematics of Operations
  Research in Dalfsen, The Netherlands}, Department of Systems Engineering and
  Computer Science, COPPE Federal University of Rio de Janeiro,
  21941~Rio~de~Janeiro, RJ, Brazil, January 1990.

\bibitem{ipm:Gonzaga4}
C.~C. Gonzaga.
\newblock Polynomial affine algorithms for linear programming.
\newblock {\em Mathematical Programming}, 49:7--21, 1990.

\bibitem{ipm:Gonzaga3}
C.~C. Gonzaga.
\newblock Interior point algorithms for linear programming problems with
  inequality constraints.
\newblock {\em Mathematical Programming}, 52:209--225, 1991.

\bibitem{ipm:Gonzaga21}
C.~C. Gonzaga.
\newblock An interior trust region method for linearly constrained
  optimization.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:55--66, August 1991.

\bibitem{ipm:Gonzaga7}
C.~C. Gonzaga.
\newblock Large steps path--following methods for linear programming,
  {Part\,I\,: Barrier} function method.
\newblock {\em SIAM Journal on Optimization}, 1:268--279, 1991.

\bibitem{ipm:Gonzaga8}
C.~C. Gonzaga.
\newblock Large steps path--following methods for linear programming,
  {Part\,II\,: Potential} reduction method.
\newblock {\em SIAM Journal on Optimization}, 1:280--292, 1991.

\bibitem{ipm:Gonzaga14}
C.~C. Gonzaga.
\newblock On lower bound updates in primal potential reduction methods for
  linear programming.
\newblock {\em Mathematical Programming}, 52:415--428, 1991.

\bibitem{ipm:Gonzaga16}
C.~C. Gonzaga.
\newblock On the convergence of the large step affine--scaling algorithm for
  linear programming.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Systems Engineering and Computer Science,
  COPPE Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil,
  July 1991.

\bibitem{ipm:Gonzaga2}
C.~C. Gonzaga.
\newblock Search directions for interior linear programming methods.
\newblock {\em Algorithmica}, 6:153--181, 1991.

\bibitem{ipm:Gonzaga23}
C.~C. Gonzaga.
\newblock Ellipsoidal trust regions and prox functions for linearly constrained
  nonlinear programs.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Systems Engineering and Computer Science, COPPE
  Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil, May
  1992.

\bibitem{ipm:Gonzaga19}
C.~C. Gonzaga.
\newblock Path following methods for linear programming.
\newblock {\em SIAM Review}, 34(2):167--227, 1992.

\bibitem{ipm:Gonzaga30}
C.~C. Gonzaga.
\newblock On the complexity of linear programming.
\newblock {\em Resenhas do Instituto de Matem{\'a}tica e Estat{\'i}st{\'i}ca da
  Universidade de S$\tilde{a}$o Paulo}, 2:197--207, 1995.

\bibitem{ipm:Gonzaga32}
C.~C. Gonzaga.
\newblock Complexity of predictor--corrector algorithms for {LCP} based on a
  large neighborhood of the central path.
\newblock {Technical Report}, Department of Mathematics, Federal University of
  Santa Catarina, 88040--970~Florianopolis, SC, Brazil, 1996.

\bibitem{ipm:Gonzaga27}
C.~C. Gonzaga.
\newblock The largest step path following algorithm for monotone linear
  complementarity problems.
\newblock {\em Mathematical Programming}, 76:309--332, 1997.

\bibitem{ipm:Gonzaga31}
C.~C. Gonzaga and J.~F. Bonnans.
\newblock Fast convergence of the simplified largest step path following
  algorithm.
\newblock {\em Mathematical Programming}, 76:95--115, 1997.

\bibitem{ipm:Gonzaga22}
C.~C. Gonzaga and L.~A. Carlos.
\newblock A primal affine--scaling algorithm for linearly constrained convex
  programs.
\newblock {Technical Report} ES--238/90, Department of Systems Engineering and
  Computer Science, COPPE Federal University of Rio de Janeiro,
  21941~Rio~de~Janeiro, RJ, Brazil, December 1990.

\bibitem{ipm:Gonzaga29}
C.~C. Gonzaga and H.~J. Lara.
\newblock A note on properties of condition numbers.
\newblock {Technical Report}, Department of Mathematics, Federal University of
  Santa Catarina, 88040--970~Florianopolis, SC, Brazil, March 1996.

\bibitem{ipm:Gonzaga26}
C.~C. Gonzaga and R.~A. Tapia.
\newblock A quadratically convergent primal--dual algorithm for linear
  programming.
\newblock {Technical Report}, Department of Mathematical Sciences, Rice
  University, Houston, TX~77251, USA, 1993.
\newblock (In preparation).

\bibitem{ipm:Gonzaga25}
C.~C. Gonzaga and R.~A. Tapia.
\newblock On the convergence of the {Mizuno--Todd--Ye} algorithm to the
  analytic center of the solution set.
\newblock {\em SIAM Journal on Optimization}, 7:47--65, 1997.

\bibitem{ipm:Gonzaga24}
C.~C. Gonzaga and R.~A. Tapia.
\newblock On the quadratic convergence of the simplified {Mizuno--Todd--Ye}
  algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 7:66--85, 1997.

\bibitem{ipm:Gonzaga12}
C.~C. Gonzaga and M.~J. Todd.
\newblock An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine
  algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:349--359, 1992.

\bibitem{ipm:GonzalezLima2}
M.~D. Gonzalez-Lima.
\newblock Effective computation of the analytic center of the solution set in
  linear programming using primal--dual interior--point methods.
\newblock {Technical Report} TR~94--48, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1994.

\bibitem{ipm:GonzalezLima3}
M.~D. Gonz{\'a}lez-Lima, R.~A. Tapia, and F.~A. Potra.
\newblock On effectively computing the analytic center of the solution set by
  primal--dual interior--point methods.
\newblock {\em SIAM Journal on Optimization}, 8:1--25, 1998.

\bibitem{ipm:GonzalezLima1}
M.~D. Gonz{\'a}lez-Lima, R.~A. Tapia, and R.~M. Thrall.
\newblock On the construction of strong complementarity slackness solutions for
  {DEA} linear programming problems using a primal--dual interior--point
  method.
\newblock {\em Annals of Operations Research}, 66:139--162, 1996.

\bibitem{ipm:Gonzalez1}
C.~{Gonzalez Martin} and M.~{Sanchez Garcia}.
\newblock The method of {Karmarkar}\,: {A} study of its variants.
\newblock {\em Trabajos de Investigacion Operativa}, 6(1):3--25, 1991.
\newblock (In Spain, English summary).

\bibitem{ipm:Granville1}
S.~Granville.
\newblock Optimal reactive dispatch through interior point methods.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:136--146, 1994.

\bibitem{ipm:Granville2}
S.~Granville, O.~C.~O. Mello, and A.~C.~G. Mello.
\newblock Application of interior point methods to power flow unsolvability.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 11:1096--1103, 1996.

\bibitem{ipm:Gray1}
P.~Gray, J.~A. Kaliski, and Y.~Ye.
\newblock An implementation of the build--up interior method for linear
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, College of Business, Department of Management Sciences,
  University of Iowa, Iowa City, IA~52242, USA, May 1991.

\bibitem{ipm:Grayson1}
M.~A. Grayson.
\newblock The basin of attraction for interior point linear programming
  algorithms.
\newblock {Research Report} RC~15969, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1990.

\bibitem{ipm:Greenberg1}
H.~J. Greenberg.
\newblock The use of the optimal partition in a linear programming solution for
  postoptimal analysis.
\newblock {\em Operations Research Letters}, 15:179--185, 1994.

\bibitem{ipm:Greenberg4}
H.~J. Greenberg.
\newblock Rim sensitivity analysis from an interior solution.
\newblock {Technical Report} CCM--86, Center of Computational Mathematics,
  Department of Mathematics, University of Colorado at Denver, Denver,
  CO~80217, USA, October 1996.

\bibitem{ipm:Greenberg2}
H.~J. Greenberg.
\newblock Matrix sensitivity analysis from an interior solution of a linear
  program.
\newblock {Technical Report}, Center of Computational Mathematics, Department
  of Mathematics, University of Colorado at Denver, Denver, CO~80217, USA,
  1997.

\bibitem{ipm:Greenberg3}
H.~J. Greenberg, A.~G. Holder, C.~Roos, and T.~Terlaky.
\newblock On the dimension of the set of rim pertubations for optimal partition
  invariance.
\newblock {\em SIAM Journal on Optimization}, 9:207--216, 1999.

\bibitem{ipm:Grigoriadis1}
M.~D. Grigoriadis and L.~G. Khachiyan.
\newblock An interior point method for bordered block--diagonal linear
  programs.
\newblock {\em SIAM Journal on Optimization}, 6:913--932, 1996.

\bibitem{ipm:Groetschel1}
M.~Gr{\"o}tschel.
\newblock {Patente f{\"u}r mathematische Algorithmen. (Patents for mathematical
  algorithms)}.
\newblock {\em Mitteilungen der Deutschen Mathematiker--Vereinigung}, {Heft
  2}:52--56, April 1991.
\newblock (In German).

\bibitem{ipm:Grover3}
L.~K. Grover.
\newblock A force based approach to interior point algorithms for linear
  programming.
\newblock {Technical Report}, School of Electrical Engineering, Cornell
  University, Ithaca, NY~14853, USA, 1990.

\bibitem{ipm:Grover2}
L.~K. Grover.
\newblock Interior point methods for unimodular linear programming.
\newblock {Technical Report}, School of Electrical Engineering, Cornell
  University, Ithaca, NY~14853, USA, 1990.

\bibitem{ipm:Grover1}
L.~K. Grover.
\newblock Strongly polynomial interior point algorithm for a class of linear
  programming problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, School of Electrical Engineering, Cornell University, Ithaca,
  NY~14853, USA, October 1990.

\bibitem{ipm:Grover4}
L.~K. Grover.
\newblock Fast interior point methods for bipartite matching.
\newblock {\em SIAM Journal on Optimization}, 5:740--769, 1995.

\bibitem{ipm:Gu1}
M.~Gu.
\newblock On primal--dual interior point methods for semidefinite programming.
\newblock {CAM Technical Report} 97--12, Department of Mathematics, University
  of California, Los Angelos, CA, USA, March 1997.

\bibitem{ipm:Gueler5}
O.~G{\"u}ler.
\newblock An interior point algorithm for nonlinear monotone complementarity
  problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, October 1990.

\bibitem{ipm:Gueler4}
O.~G{\"u}ler.
\newblock Path following and potential reduction algorithms for nonlinear
  monotone complementarity problems.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1991.

\bibitem{ipm:Gueler8}
O.~G{\"u}ler.
\newblock Generalized linear complementarity problems and interior point
  algorithms for their solutions.
\newblock {Technical Report}, Faculty of Technical Mathematics and Computer
  Science, TU Delft, NL--2600~GA~Delft, The Netherlands, April 1992.
\newblock See also G{\"u}ler \cite{ipm:Gueler14}.

\bibitem{ipm:Gueler11}
O.~G{\"u}ler.
\newblock Complexity of smooth convex programming and its applications.
\newblock In P.~M. Pardalos, editor, {\em Complexity in Numerical
  Optimization}, pages 180--202. World Scientific Publishing Co., London,
  United Kingdom, 1993.

\bibitem{ipm:Gueler2}
O.~G{\"u}ler.
\newblock Existence of interior points and interior paths in nonlinear monotone
  complementarity problems.
\newblock {\em Mathematics of Operations Research}, 18(1):128--147, 1993.

\bibitem{ipm:Gueler9}
O.~G{\"u}ler.
\newblock Limiting behavior of the weighted central paths in linear
  programming.
\newblock {\em Mathematical Programming}, 66:347--363, 1994.

\bibitem{ipm:Gueler14}
O.~G{\"u}ler.
\newblock Generalized linear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 20:441--448, 1995.
\newblock See also G{\"u}ler \cite{ipm:Gueler8}.

\bibitem{ipm:Gueler10}
O.~G{\"u}ler.
\newblock Barrier functions in interior point methods.
\newblock {\em Mathematics of Operations Research}, 21:860--885, 1996.

\bibitem{ipm:Gueler15}
O.~G{\"u}ler.
\newblock Hyperbolic polynomials and interior point methods for convex
  programming.
\newblock {\em Mathematics of Operations Research}, 22:350--377, 1997.

\bibitem{ipm:Gueler13}
O.~G{\"u}ler.
\newblock On the self--concordance of the universal barrier function.
\newblock {\em SIAM Journal on Optimization}, 7:295--303, 1997.

\bibitem{ipm:Gueler6}
O.~G{\"u}ler, {D. den} Hertog, C.~Roos, T.~Terlaky, and T.~Tsuchiya.
\newblock Degeneracy in interior point methods for linear programming.
\newblock {\em Annals of Operations Research}, 46/47:107--138, 1993.

\bibitem{ipm:Gueler7}
O.~G{\"u}ler, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock Interior point approach to the theory of linear programming.
\newblock {Cahiers de Recherche} 1992.3, Faculte des Sciences Economique et
  Sociales, Universite de Geneve, Geneve, Switzerland, 1992.
\newblock To appear in {\em Management Science}.

\bibitem{ipm:Gueler16}
O.~G{\"u}ler, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock A survey of the implications of the behavior of the central path for
  the duality theory of linear programming.
\newblock {\em Management Science}, 41:1922--1934, 1995.

\bibitem{ipm:Gueler17}
O.~G{\"u}ler and L.~Tun{\c c}el.
\newblock Invariant barrier functions on homogeneous cones.
\newblock {Research Report}, Department of Combinatorics and Optimization,
  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada,
  1997.
\newblock (In preparation).

\bibitem{ipm:Gueler12}
O.~G{\"u}ler and L.~Tun{\c c}el.
\newblock Characterization of the barrier parameter of homogeneous convex
  cones.
\newblock {\em Mathematical Programming}, 81:55--76, 1998.

\bibitem{ipm:Gueler3}
O.~G{\"u}ler and Y.~Ye.
\newblock Convergence behavior of some interior point algorithms.
\newblock {Working Paper} 91--04, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.
\newblock To appear in {\em Mathematical Programming 1993}.

\bibitem{ipm:Gueler1}
O.~G{\"u}ler and Y.~Ye.
\newblock Interior point algorithms for {LP} generate strictly complementary
  solutions.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Management Science, University of Iowa, Iowa
  City, IA~52242, USA, May 1991.

\bibitem{ipm:Guenzel1}
H.~G{\"u}nzel.
\newblock Linear programming\,: {The} central path extends analytically.
\newblock {Preprint}~67, Lehrstuhl C f{\"u}r Mathematik, RWTH Aachen,
  Templergraben 55, D--52056 Aachen, Germany, February 1996.

\bibitem{ipm:Guo4}
T.-D. Guo.
\newblock An interior point method for convex quadratic programming based on
  predictor--corrector procedure.
\newblock {\em J. Qufu Norm. Univ., Nat. Sci.}, 21:1--6, 1995.
\newblock (In Chinese).

\bibitem{ipm:Guo7}
T.-D. Guo and F.~Wu.
\newblock Interior ellipsoid method for convex quadratic programming.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
  19(?):46--50, 1996.

\bibitem{ipm:Guo8}
T.-D. Guo and F.~Wu.
\newblock An extension of predictor--corrector algorithm to a class of convex
  separable program.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
  13:362--370, 1997.

\bibitem{ipm:Guo6}
T.-D. Guo and S.~Wu.
\newblock A modified homogeneous and self--dual linear programming algorithm.
\newblock {\em Systems Science and Mathematical Sciences}, 8:270--277, 1995.

\bibitem{ipm:Guo5}
T.-D. Guo and S.~Wu.
\newblock Properties of primal interior point methods for {QP}.
\newblock {\em Optimization}, 37:227--238, 1996.

\bibitem{ipm:Guo2}
T.-D. Guo and S.-Q. Wu.
\newblock An interior point algorithm for convex programming.
\newblock {\em Qufu Shifan Daxue Xuebao Ziran Kexue Ban}, 20(Suppl.):1--7,
  1994.
\newblock (In Chinese, English summary).

\bibitem{ipm:Guo3}
T.-D. Guo and S.-Q. Wu.
\newblock Interior point methods for convex quadratic programming.
\newblock {\em Qufu Shifan Daxue Xuebao Ziran Kexue Ban}, 20:51--62, 1994.
\newblock (In Chinese, English summary).

\bibitem{ipm:Guo1}
T.-D. Guo and S.-Q. Wu.
\newblock Predictor--corrector algorithm for convex quadratic programming with
  upper bounds.
\newblock {\em Journal of Computational Mathematics}, 13:161--171, 1995.

\bibitem{ipm:Gupta1}
A.~Gupta.
\newblock Graph partitioning based sparse matrix orderings for interior--point
  algorithms.
\newblock {Technical Report} RC\,20467\,(90480), IBM Research Division,
  T.\,J.\,Watson Research Center, Yorktown Heights, New York, NY~10598, May
  1996.

\bibitem{ipm:Gupta3}
S.~Gupta and N.~S. Chaudhari.
\newblock Study and implementation of a primal--dual
  infeasible--interior--point algorithm.
\newblock {\em Proceedings of the Mathematical Society}, 12:41--46, 1996.

\bibitem{ipm:Gupta2}
S.~Gupta and N.~S. Chaudhari.
\newblock A primal--dual formulation of general linear programming problem for
  {Karmarkar's} approach.
\newblock {\em Journal of the Indian Academical Mathematics}, 19:223--230,
  1997.

\bibitem{ipm:Haeberly2}
J.-P.~A. Haeberly, M.~Nayakkankuppam, and M.~L. Overton.
\newblock Extending {Mehrotra and Gondzio} higher order methods to mixed
  semidefinite--quadratic--linear programming.
\newblock {\em Optimization Methods and Software}, 1998/99.

\bibitem{ipm:Haeberly1}
J.-P.~A. Haeberly and M.~L. Overton.
\newblock Optimizing eigenvalues of symmetric definite pencils.
\newblock {\em Proceedings of the 1994 American Control Conference (Baltimore,
  MD, USA, June/July 1994)}, 1:836--839, 1994.

\bibitem{ipm:Hafsteinsson1}
H.~Hafsteinsson, R.~Levkovitz, and G.~Mitra.
\newblock Solving large scale linear programming problems using an interior
  point method on a massively parallel {SIMD} computer.
\newblock volume~4 of {\em Applied Parallel Computing}, pages 301--316. Gordon
  and Breach Publishers, London, United Kingdom, 1993.

\bibitem{ipm:Haglin1}
D.~Haglin, J.~Kaliski, C.~Roos, and T.~Terlaky.
\newblock Logarithmic barrier decomposition methods for semi--definite
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\newblock {Technical Report} 96--51, Faculty of Technical Mathematics and
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\newblock Rewritten in den Hertog et al.\ \cite{ipm:Hertog12}.

\bibitem{ipm:Hertog15}
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\bibitem{ipm:Hertog14}
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\newblock Revised version of {Technical Report} 89--85, Faculty of Mathematics
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S.~Huang, J.~Ji, and F.~Potra.
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\newblock {Working Paper Series} 89--2, College of Business Administration,
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\newblock {Working Paper Series} 91--16, Department of Management Sciences,
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  Simplexverfahrens und von Innere--Punkte--Verfahren (Bounds for the average
  running time of the simplex--method and od interior--point methods)}}.
\newblock PhD thesis, Mathematische Naturwissentschaftliche Fakult{\"a}t,
  Universit{\"a} Augsburg, Augsburg, Germany, August 1997.
\newblock In German, English Summary. Published as\,: {\it{Augsburger
  Mathematisch--Naturwissentschaftliche Schriften 16, 223pp., Dr.\, Bernd
  Wi{\ss}ner Verlag, Augsburg, Germany, ISBN\,3--89639--067--8, 1997}}.

\bibitem{ipm:Hung1}
P.~F. Hung and Y.~Ye.
\newblock An asymptotically {$O(\sqrt{n}L)$} iteration algorithm that uses long
  steps.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, March 1994.
\newblock See also Hung and Ye \cite{ipm:Hung2}.

\bibitem{ipm:Hung2}
P.~F. Hung and Y.~Ye.
\newblock An asymptotical $o(\sqrt{n}l)$--iteration path--following linear
  programming algorithm that uses wide neighborhoods.
\newblock {\em SIAM Journal on Optimization}, 6:570--586, 1996.

\bibitem{ipm:Hurd1}
J.~K. Hurd and F.~H. Murphy.
\newblock Exploiting special structure in primal dual interior point methods.
\newblock {\em ORSA Journal on Computing}, 4:38--44, 1992.

\bibitem{ipm:Hwang1}
T.-M. Hwang, C.-H. Lin, W.-W. Lin, and S.-C. Fang.
\newblock A relaxed primal--dual path following algorithm for linear
  programming.
\newblock {\em Annals of Operations Research}, 62:173--196, 1996.

\bibitem{ipm:IBM1}
{\emph{Optimization Subroutine Library (OSL)\,: Guide and References}}.
\newblock Manual, IBM Corporation, Kingston, USA, 1991.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Ignizio1}
J.~P. Ignizio and T.~M. Cavalier.
\newblock {\em {Linear Programming}}, chapter 7\,: {Alternatives} to the
  simplex algorithm, pages 247--271.
\newblock Prentice Hall, Englewood Cliffs, NJ~07632, USA, 1994.

\bibitem{ipm:Ikura1}
Y.~Ikura and D.~Stein.
\newblock Computational experience with a {Karmarkar--based} approach to solve
  multi--period, multi--refinery production models.
\newblock {Talk held at the 12th Triennial Conference on Operations Research in
  Athens, Greece}, AT~\&~T~Bell Laboratories, June 1990.

\bibitem{ipm:Illes2}
T.~Ill{\'e}s, J.~Peng, C.~Roos, and T.~Terlaky.
\newblock A strongly polynomial rounding procedure yielding a maximally
  complementary solution for {$P_*(\kappa)$} linear complementarity problems.
\newblock {Technical Report} 98--15, Faculty of Information Technology and
  Systems Subfaculty of Technical Mathematics and Informatics, Department of
  Statistics, Stochastic and Operations Research, Delft University of
  Technology,, P.O. Box 5031, 2600 GA Delft, The Netherlands, July 1998.

\bibitem{ipm:Illes1}
T.~Ill{\'e}s, C.~Roos, and T.~Terlaky.
\newblock Polynomial affine--scaling algorithms for ${P_{*}(\kappa)}$ linear
  complementarity problems.
\newblock In P.~Gritzmann, R.~Horst, E.~Sachs, and R.~Tichatschke, editors,
  {\em {Recent Advances in Optimization (Trier, Germany, 1996)}}, volume 452 of
  {\em Lecture Notes in Economics and Mathematical Systems}, pages 119--137.
  Springer Verlag, Berlin, Germany, 1997.

\bibitem{ipm:Imae1}
J.~Imae, T.~Furudate, and S.~Sugawara.
\newblock A simple numerical method for minimizing the maximum eigenvalues of
  symmetric matrices via nonlinear differential equation solvers.
\newblock {\em Proceedings of the 35th IEEE conference on Decision and
  Control}, 4/4:4514--4525, 1996.

\bibitem{ipm:Imai1}
H.~Imai.
\newblock Extensions of the multiplicative penalty function for linear
  programming.
\newblock {\em Journal of the Operations Research Society of Japan},
  30:160--179, 1987.

\bibitem{ipm:Imai2}
H.~Imai.
\newblock On the convexity of the multiplicative version of {Karmarkar's}
  potential function.
\newblock {\em Mathematical Programming}, 40:29--32, 1988.

\bibitem{ipm:Imai3}
H.~Imai.
\newblock Recent trends in linear programming.
\newblock {\em Journal of the Institute of Electronics, Information and
  Communication Engineers (Japan)}, 72(10):1053--1058, 1989.
\newblock (In Japanese).

\bibitem{ipm:Imai4}
H.~Imai.
\newblock On the polynomiality of the multiplicative penalty function method
  for linear programming and related inscribed ellipsoids.
\newblock {\em Transactions of the Institute of Electronics, Information and
  Communication Engineers (Japan)}, E74(4):669--671, April 1991.

\bibitem{ipm:Iri1}
M.~Iri.
\newblock Another 'simple and fast' algorithm for linear programming.
\newblock {Talk held at the 12th Symposium on Mathematical Programming in
  Cambridge, MA, USA}, Department of Mathematical Engineering and
  Instrumentation Physics, University of Tokyo, Tokyo, Japan, 1985.

\bibitem{ipm:Iri2}
M.~Iri.
\newblock Integrability of vector and polyvector fields associated with
  interior point methods.
\newblock {\em Mathematical Programming}, 52:511--525, 1991.

\bibitem{ipm:Iri6}
M.~Iri.
\newblock A proof of the polynomiality of the {Iri--Imai} method for linear
  programming.
\newblock {\em Journal of Complexity}, 9:269--290, 1993.

\bibitem{ipm:Iri3}
M.~Iri and H.~Imai.
\newblock A multiplicative penalty function for linear programming-- another
  ''new and fast'' algorithm.
\newblock {\em Proceedings of the 6th Mathematical Programming Symposium of
  Japan, Tokyo, Japan}, pages 97--120, 1985.

\bibitem{ipm:Iri4}
M.~Iri and H.~Imai.
\newblock A multiplicative barrier function method for linear programming.
\newblock {\em Algorithmica}, 1(4):455--482, 1986.

\bibitem{ipm:Iri5}
M.~Iri and H.~Imai.
\newblock Theory of the multiplicative penalty function method for linear
  programming.
\newblock In D.~S. Johnson, T.~Nishizeki, A.~Nozaki, and H.~S. Wilf, editors,
  {\em Discrete Algorithms and Complexity\,: Proceedings of the Japan--US Joint
  Seminar, Kyoto, Japan, June 1986}, pages 417--435. Academic Press, New York,
  1987.

\bibitem{ipm:Irisarri2}
G.~D. Irisarri, L.~M. Kimball, K.~A. Clements, A.~Bagchi, and P.~W. Davis.
\newblock Economic dispatch with network and ramping constraints via interior
  point methods.
\newblock {\em IEEE Transactions on Power Systems}, 13:236--242, 1998.

\bibitem{ipm:Irisarri1}
G.~D. Irisarri, X.~Wang, J.~Tong, and S.~Mokhtari.
\newblock Maximum loadability of power systems using interior point nonlinear
  optimization method.
\newblock {\em IEEE Transactions on Power Systems}, 12:162--172, 1997.

\bibitem{ipm:Ishihara1}
T.~Ishihara and M.~Kojima.
\newblock On the {\em big m} in the affine scaling algorithm.
\newblock {\em Mathematical Programming}, 62:85--93, 1993.

\bibitem{ipm:Ito3}
S.~Ito.
\newblock An interior point method for linear programming problems on a
  function space.
\newblock {\em Proceedings of the Institute Statistical Mathematics},
  42:239--246, 1994.
\newblock (In Japanese).

\bibitem{ipm:Ito2}
S.~Ito.
\newblock A primal--dual interior--point algorithm for state--constrained {LQ}
  optimal control problems.
\newblock {\em Proceedings of the 1995 American Control Conference (Seattle,
  WA, USA, June 1995)}, 3:2077--2078, 1995.

\bibitem{ipm:Ito1}
S.~Ito, C.~T. Kelley, and E.~W. Sachs.
\newblock Inexact primal--dual interior point iteration for linear programs in
  function spaces.
\newblock {\em Computational Optimization and Applications}, 4:189--201, 1995.

\bibitem{ipm:Iusem4}
A.~Iusem and R.~D.~C. Monteiro.
\newblock On dual convergence of the generalized proximal point method with
  {Bregman} distances.
\newblock {Manuscript}, School of Industrial and Systems Engineering, Georgia
  Institute of Technology, Atlanta, GA~30322, USA, October 1997.

\bibitem{ipm:Iusem1}
A.~N. Iusem.
\newblock An interior point multiplicative method for optimization under
  positivity constraints.
\newblock {\em Acta Applicatae Mathematicae}, 38:163--184, 1995.

\bibitem{ipm:Iusem3}
A.~N. Iusem.
\newblock An interior point method for the nonlinear complementarity problem.
\newblock {\em Applied Numerical Mathematics}, 24:469--482, 1997.

\bibitem{ipm:Iusem2}
A.~N. Iusem, B.~F. Svaiter, and M.~Teboulle.
\newblock Multiplicative interior gradient methods for minimization over the
  nonnegative orthant.
\newblock {\em SIAM Journal on Control and Optimization}, 34:389--406, 1996.

\bibitem{ipm:Izhutkin1}
V.~S. Izhutkin, M.~V. Petropavlovski{\v{o}}, and A.~V. Blinov.
\newblock The center and the barrier function methods using reduced directions
  for the nonlinear programming problem.
\newblock {\em Izvestiya Vyssihikh Uchebnykh Zavedemi{\v{i}} Matematika}, pages
  30--41, 1996.
\newblock (In Russian. Translated in {\emph{Russian Mathematics}}).

\bibitem{ipm:Jamsek1}
J.~Jam{\u{s}}ek.
\newblock Karmarkar's algorithm for linear programming.
\newblock {\em Obzornik za Matematiko in Fiziko}, 38(6):161--169, 1991.
\newblock (In Slovenian, English summary).

\bibitem{ipm:Jan3}
G.~M. Jan.
\newblock {\em A new variant of the primal affine scaling algorithm for linear
  programs}.
\newblock PhD thesis, Department of Operations Research, North Carolina State
  University, Raleigh, NC~27695-7913, USA, July 1990.

\bibitem{ipm:Jan1}
G.~M. Jan and S.-C. Fang.
\newblock A variant of affine--scaling method for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, North Carolina State University, Raleigh, NC~27695-7913, USA, October
  1989.
\newblock See Jan \cite{ipm:Jan3}, and Jan and Fang \cite{ipm:Jan2}.

\bibitem{ipm:Jan2}
G.~M. Jan and S.-C. Fang.
\newblock A new variant of the primal affine scaling method for linear
  programs.
\newblock {\em Optimization}, 22(5):681--715, 1991.

\bibitem{ipm:Janacek1}
J.~Janacek.
\newblock {Perspektivy Karmarkarova algorithmu v linearnim programovani
  (Perspectives of Karmarkar's algorithm in linear programming)}.
\newblock {\em Ekonomicko--Matematicky Obzor (Czechoslovakia)}, 25(1):50--63,
  1989.
\newblock (In Czech).

\bibitem{ipm:Jansen6}
B.~Jansen.
\newblock An introduction to interior point algorithms for linear and convex
  quadratic programming.
\newblock {Technical Report} 9276/A, Economic Institute, Erasmus University
  Rotterdam, NL--3000~DR~Rotterdam, The Netherlands, 1992.

\bibitem{ipm:Jansen19}
B.~Jansen.
\newblock {\em {Interior Point Techniques in Optimization\,: Complexity,
  Sensitivity and Algorithms}}, volume~6 of {\em Applied Optimization}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.

\bibitem{ipm:Jansen12}
B.~Jansen, {J. J. de} Jong, C.~Roos, and T.~Terlaky.
\newblock Sensitivity analysis in linear programming\,: {Just} be careful\,!
\newblock {\em European Journal of Operational Research}, 101:15--28, 1997.

\bibitem{ipm:Jansen1}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock An interior point approach to postoptimal and parametric analysis in
  linear programming.
\newblock {Technical Report} 92--21, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2628~CD~Delft, The Netherlands, April 1992.
\newblock New subtitle: {\em Optimal bases versus optimal partitions for
  postoptimal analysis in linear programming}.

\bibitem{ipm:Jansen5}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock On {Vaidya's} volumetric center method for convex programming.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 289--295. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Jansen3}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Primal--dual algorithms for linear programming based on the
  logarithmic barrier method.
\newblock {\em Journal of Optimization Theory and Applications}, 83:1--26,
  1994.

\bibitem{ipm:Jansen4}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock The theory of linear programming\,: {Skew} symmetric self--dual
  problems and the central path.
\newblock {\em Optimization}, 29:225--233, 1994.

\bibitem{ipm:Jansen14}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A new algorithm for the computation of the smallest eigenvalue of a
  symmetric matrix and its eigenspace.
\newblock {Technical Report} 95--70, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Jansen13}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A short survey on ten years interior point methods.
\newblock {Technical Report} 95--45, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Jansen16}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Interior point methods, a decade after {Karmarkar} -- {A} survey,
  with application to the smallest eigenvalue problem.
\newblock {\em Statistica Nederlandica}, 50:146--170, 1996.

\bibitem{ipm:Jansen17}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Introduction to the theory of interior point methods.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 3--34. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Jansen10}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Long--step primal--dual target--following algorithms for linear
  programming.
\newblock {\em Mathematical Models of Operations Research}, 44:11--30, 1996.

\bibitem{ipm:Jansen7}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A polynomial primal--dual {Dikin}--type algorithm for linear
  programming.
\newblock {\em Mathematics of Operations Research}, 21:341--353, 1996.

\bibitem{ipm:Jansen18}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock Target--following methods for linear programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 83--124. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Jansen9}
B.~Jansen, C.~Roos, and T.~Terlaky.
\newblock A family of polynomial affine scaling algorithms for positive
  semidefinite linear complementarity problems.
\newblock {\em SIAM Journal on Optimization}, 7:126--140, 1997.

\bibitem{ipm:Jansen2}
B.~Jansen, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock Interior--point methodology for linear programming\,:\, {Duality},
  sensitivity analysis and computational aspects.
\newblock In K.~Frauendorfer, H.~Glavitsch, and R.~Bacher, editors, {\em
  Optimization in Planning and Operation of Electric Power Systems (Lecture
  Notes of the SVOR/ASRO Tutorial, Thun, Switzerland, October 14--16, 1992)},
  pages 57--123. Physica Verlag (A Springer Company), Heidelberg, Germany,
  1993.
\newblock See also Roos \cite{ipm:Roos21}.

\bibitem{ipm:Jansen8}
B.~Jansen, C.~Roos, T.~Terlaky, and J.-Ph. Vial.
\newblock Primal--dual target--following algorithms for linear programming.
\newblock {\em Annals of Operations Research}, 62:197--231, 1996.

\bibitem{ipm:Jansen11}
B.~Jansen, C.~Roos, T.~Terlaky, and Y.~Ye.
\newblock Improved complexity using higher--order correctors for primal--dual
  {Dikin} affine scaling.
\newblock {\em Mathematical Programming}, 76:117--130, 1997.

\bibitem{ipm:Jansen15}
B.~Jansen, C.~Roos, T.~Terlaky, and A.~Yoshise.
\newblock Polynomiality of primal--dual affine scaling algorithms for nonlinear
  complementarity problems.
\newblock {\em Mathematical Programming}, 78:315--345, 1997.

\bibitem{ipm:Jarre14}
F.~Jarre.
\newblock On the convergence of the method of analytic centers when applied to
  convex quadratic programs.
\newblock {DFG--Report}~35, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, 1987.
\newblock Preliminary version of Jarre \cite{ipm:Jarre1}.

\bibitem{ipm:Jarre6}
F.~Jarre.
\newblock Convergence of the method of analytic centers for generalized convex
  programs.
\newblock DFG--Report~67, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany, May
  1988.
\newblock Revised October 1988. The revised version is identical to Jarre
  \cite{ipm:Jarre3}.

\bibitem{ipm:Jarre2}
F.~Jarre.
\newblock The method of analytic centers for smooth convex programs.
\newblock Preprint 165, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  February 1989.
\newblock See also Jarre \cite{ipm:Jarre7}.

\bibitem{ipm:Jarre7}
F.~Jarre.
\newblock {\em The method of analytic centers for smooth convex programs}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  1989.

\bibitem{ipm:Jarre3}
F.~Jarre.
\newblock On the method of analytic centers for solving smooth convex programs.
\newblock In S.~Dolecki, editor, {\em Optimization\,: Proceedings of the 5th
  French--German Conference in Castel--Novel, Varetz, France, October 1988},
  volume 1405 of {\em Lecture Notes in Mathematics}, pages 69--86. Springer
  Verlag, Berlin, Germany, 1989.

\bibitem{ipm:Jarre4}
F.~Jarre.
\newblock A homotopy method for convex programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  January 1990.

\bibitem{ipm:Jarre8}
F.~Jarre.
\newblock Interior--point methods for convex programming.
\newblock {Technical Report} SOL~90--16, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, 1990.
\newblock See also Jarre \cite{ipm:Jarre15}.

\bibitem{ipm:Jarre1}
F.~Jarre.
\newblock On the convergence of the method of analytic centers when applied to
  convex quadratic programs.
\newblock {\em Mathematical Programming}, 49:341--358, 1990/91.

\bibitem{ipm:Jarre17}
F.~Jarre.
\newblock An efficient line--search for logarithmic barrier functions.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD '93), Budapest, Hungary, January 1993, Volume
  of Extended Abstracts}, pages 296--303. Computer and Automation Institute,
  Hungarian Academy of Sciences, Budapest, Hungary, December 1992.
\newblock See also Jarre \cite{ipm:Jarre13}.

\bibitem{ipm:Jarre13}
F.~Jarre.
\newblock An efficient line search for logarithmic barrier functions.
\newblock {Technical Report} 188, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, May 1992.
\newblock For an extended abstract see Jarre \cite{ipm:Jarre17}.

\bibitem{ipm:Jarre15}
F.~Jarre.
\newblock Interior--point methods for convex programming.
\newblock {\em Applied Mathematics \& Optimization}, 26:287--311, 1992.
\newblock See also Jarre \cite{ipm:Jarre8}.

\bibitem{ipm:Jarre11}
F.~Jarre.
\newblock An interior--point method for minimizing the largest eigenvalue of a
  linear combination of matrices.
\newblock {\em SIAM Journal on Control and Optimization}, 31:1360--1377, 1993.
\newblock See also {\em NATO ASI Series E Vol.\,232 (1993), pp. 395}.

\bibitem{ipm:Jarre22}
F.~Jarre.
\newblock Interior--point methods via self--concordance or relative {Lipschitz}
  condition.
\newblock {Habilitationthesis}, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, March 1994.
\newblock See also Jarre \cite{ipm:Jarre21}.

\bibitem{ipm:Jarre19}
F.~Jarre.
\newblock A new line--search step based on the {Weierstrass}
  ${\cal{p}}$--function for minimizing a class of logarithmic barrier
  functions.
\newblock {\em Numerische Mathematik}, 68:81--94, 1994.

\bibitem{ipm:Jarre16}
F.~Jarre.
\newblock Optimal ellipsoidal approximations around the analytic center.
\newblock {\em Applied Mathematics \& Optimization}, 30:15--19, 1994.

\bibitem{ipm:Jarre21}
F.~Jarre.
\newblock Interior--point methods via self--concordance or relative {Lipschitz}
  condition.
\newblock {\em Optimization Methods and Software}, 5:75--104, 1995.
\newblock See also Jarre \cite{ipm:Jarre22}.

\bibitem{ipm:Jarre23}
F.~Jarre.
\newblock Interior--point methods for classes of convex programs.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 255--296. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Jarre26}
F.~Jarre.
\newblock A {QQP}--minimization method for semidefinite and smooth nonconvex
  programs.
\newblock {Technical Report}, Mathematisches Institut der Universit{\"a}t
  Trier, Trier, Germany, August 1998.

\bibitem{ipm:Jarre24}
F.~Jarre, M.~Kocvara, and J.~Zowe.
\newblock Interior point methods for mechanical design problems.
\newblock {Preprint} 173, Institut f{\"u}r Angewandte Mathematik,
  Universit{\"a}t Erlangen--N{\"u}rnberg, Martensstr. 3, D--91058 Erlangen,
  Germany, 1996.

\bibitem{ipm:Jarre27}
F.~Jarre, M.~Kocvara, and J.~Zowe.
\newblock Optimal truss design by interior--point methods.
\newblock {\em SIAM Journal on Optimization}, 8:1084--1107, 1998.

\bibitem{ipm:Jarre18}
F.~Jarre and S.~Mizuno.
\newblock An infeasible--interior--point algorithm using projections onto a
  convex set.
\newblock {Technical Report} 206, Institut f{\"u}r Angewandte Mathematik und
  Statistik, Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg,
  Germany, August 1993.
\newblock See also Mizuno and Jarre \cite{ipm:Mizuno23}.

\bibitem{ipm:Jarre10}
F.~Jarre and M.~A. Saunders.
\newblock An adaptive primal--dual method for linear programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:7--16, August 1991.

\bibitem{ipm:Jarre12}
F.~Jarre and M.~A. Saunders.
\newblock A practical interior--point method for convex programming.
\newblock {\em SIAM Journal on Optimization}, 5:149--171, 1995.

\bibitem{ipm:Jarre5}
F.~Jarre, G.~Sonnevend, and J.~Stoer.
\newblock An implementation of the method of analytic centers.
\newblock In A.~Bensoussan and J.~L. Lions, editors, {\em Analysis and
  Optimization of Systems}, volume 111 of {\em Lecture Notes in Control and
  Information Sciences}, pages 297--308. Springer Verlag, Berlin, Germany,
  1988.

\bibitem{ipm:Jarre9}
F.~Jarre, G.~Sonnevend, and J.~Stoer.
\newblock On the complexity of a numerical algorithm for solving generalized
  convex quadratic programs by following a central path.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 233--242. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Jarre25}
F.~Jarre and M.~Wechs.
\newblock Extending {Mehrotra's} corrector for linear programs.
\newblock {Preprint} 219, Mathematische Institute der Universit{\"a}t
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\newblock The convergence of a modified barrier method for convex programming.
\newblock {\em IBM Journal of Research and Development}, 38:307--321, 1994.

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D.~L. Jensen and A.~E. Steger.
\newblock A variation of {Karmarkar's} algorithm to solve linear programs in
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Los Angeles,
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\newblock See Steger \cite{ipm:Steger1}.

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\newblock {Reports on Computational Mathematics}~25, Department of Mathematics,
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\newblock {\em Journal of Optimization Theory and Applications}, 77:79--95,
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\newblock {Reports on Computational Mathematics}~98, Department of Mathematics,
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\newblock {Technical Report} TR--91--23, Department of Mathematical Sciences,
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\newblock {Working Paper} 90--5, Department of Mathematics, The University of
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\newblock {Science Report} 96009, Department of Applied Mathematics, Tsinghue
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\newblock To appear in {\em{Operations Research Letters}}.

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\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
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\newblock {Technical Report} 96--51, Faculty of Technical Mathematics and
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A.~P. Kamath, N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
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\newblock {\em Journal of Optimization Theory and Applications}, 98:399--429,
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\newblock {\em Proceedings of the 18th Annual ACM Symposium on Theory of
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S.~Kapoor and P.~M. Vaidya.
\newblock An extension of {Karmarkar's} interior point method to convex
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\newblock {Technical Report}, Department of Computer Science, University of
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\bibitem{ipm:Kapoor3}
S.~Kapoor and P.~M. Vaidya.
\newblock Speeding--up {Karmarkar's} algorithm for multicommodity flows.
\newblock {\em Mathematical Programming}, 73:111--127, 1996.
\newblock A preliminary version is given in Kapoor and Vaidya
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S.~E. Karisch and F.~Rendl.
\newblock Semidefinite programming and graph equipartion.
\newblock {Technical Report} 302--CDLDO~55, Department of Mathematics, Graz
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S.~E. Karisch, F.~Rendl, and J.~Clausen.
\newblock Solving graph bisection problems with semidefinite programming.
\newblock {Technical Report} DIKU--TR--97/9, Department of Computer Science,
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\bibitem{ipm:Karisch3}
S.~E. Karisch, F.~Rendl, H.~Wolkowicz, and Q.~Zhao.
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\newblock {Technical Report} CORR\,95--27, Department of Combinatorics and
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H.~Karloff.
\newblock {\em Linear Programming}, chapter 5\,: {Karmarkar's} algorithm, pages
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\newblock Birkh{\"a}user Verlag, Basel, Switzerland, 1991.

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N.~K. Karmarkar.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {\em Proceedings of the 16th Annual ACM Symposium on Theory of
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\bibitem{ipm:Karmarkar2}
N.~K. Karmarkar.
\newblock A new polynomial--time algorithm for linear programming.
\newblock {\em Combinatorica}, 4:373--395, 1984.

\bibitem{ipm:Karmarkar3}
N.~K. Karmarkar.
\newblock Some comments on the significance of the new polynomial--time
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\newblock {Technical Report}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974,
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\bibitem{ipm:Karmarkar18}
N.~K. Karmarkar.
\newblock Why is the new algorithm better than simplex method and ellipsoid
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\newblock {Extended Abstract}, AT~\&~T~Bell Laboratories, Murray Hill,
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\bibitem{ipm:Karmarkar16}
N.~K. Karmarkar.
\newblock Recent developments in new approaches to linear programming.
\newblock {Talk held at the SIAM Conference on Optimization, Houston, TX, USA},
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\bibitem{ipm:Karmarkar4}
N.~K. Karmarkar.
\newblock An interior--point approach to {NP}--complete problems.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA, July 1988.

\bibitem{ipm:Karmarkar5}
N.~K. Karmarkar.
\newblock Methods and apparatus for efficient resource allocation.
\newblock U.S.~Patent No.~4.744.028, 1988.
\newblock AT~\&~T Bell Laboratories, Murray Hill, NJ~07974, USA.

\bibitem{ipm:Karmarkar19}
N.~K. Karmarkar.
\newblock An interior--point approach to {NP}--complete problems -- {Part I}.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\bibitem{ipm:Karmarkar6}
N.~K. Karmarkar.
\newblock Riemannian geometry underlying interior--point methods for linear
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\bibitem{ipm:Karmarkar22}
N.~K. Karmarkar.
\newblock A new parallel architecture for sparse matrix computation based on
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\bibitem{ipm:Karmarkar15}
N.~K. Karmarkar.
\newblock Interior--point methods in optimization.
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\bibitem{ipm:Karmarkar14}
N.~K. Karmarkar, J.~C. Lagarias, L.~Slutsman, and P.~Wang.
\newblock Power--series variants of {Karmarkar--type} algorithms.
\newblock {\em AT~\&~T Technical Journal}, 68:20--36, 1989.

\bibitem{ipm:Karmarkar7}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Further developments in the new polynomial--time algorithm for linear
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Boston, MA,
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\bibitem{ipm:Karmarkar8}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Implementation and computational aspects of the {Karmarkar} algorithm
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\newblock {Technical Memorandum}, AT~\&~T Bell Laboratories, Murray Hill,
  NJ~07974, USA, 1989.
\newblock See Karmarkar and Ramakrishnan \cite{ipm:Karmarkar9}.

\bibitem{ipm:Karmarkar10}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Robust control system models and their solution by the {Karmarkar}
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\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, AT~\&~T
  Bell Laboratories, Murray Hill, NJ~07974, USA, July 1990.

\bibitem{ipm:Karmarkar9}
N.~K. Karmarkar and K.~G. Ramakrishnan.
\newblock Computational results of an interior point algorithm for large scale
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\newblock {\em Mathematical Programming}, 52:555--586, 1991.

\bibitem{ipm:Karmarkar12}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior point algorithm for zero--one integer programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, AT~\&~T Bell Laboratories, Murray Hill, NJ 07974, USA, October 1988.

\bibitem{ipm:Karmarkar20}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock An interior--point approach to the maximum independent set problem in
  dense random graphs.
\newblock {Manuscript}, AT~\&~T~Bell Laboratories, Murray Hill, NJ~07974, USA,
  1988/1990.

\bibitem{ipm:Karmarkar13}
N.~K. Karmarkar, K.~G. Ramakrishnan, and M.~G.~C. Resende.
\newblock Further developments on an interior point algorithm for zero--one
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\newblock {Talk held at the First International Symposium on Interior Point
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\bibitem{ipm:Karmarkar17}
N.~K. Karmarkar, M.~G.~C. Resende, and K.~G. Ramakrishnan.
\newblock An interior point algorithm to solve computationally difficult set
  covering problems.
\newblock {\em Mathematical Programming}, 52:597--618, 1991.

\bibitem{ipm:Karmarkar11}
N.~K. Karmarkar and L.~P. Sinha.
\newblock Application of {Karmarkar's} algorithm to overseas telecommunications
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\newblock {Talk held at the 12th International Symposium on Mathematical
  Programming in Boston, MA, USA}, AT~\&~T Bell Laboratories, Murray Hill,
  NJ~07974, USA, August 1985.

\bibitem{ipm:Karmarkar21}
N.~K. Karmarkar and S.~Thakur.
\newblock An interior--point approach to tensor optimization with application
  to upper bounds in integer quadratic optimization problems.
\newblock {\em Proceedings of Second Integer programming and Combinatorial
  Optimization Conference (Carnegie--Mellon University, Pittsburgh, PA, 1992)},
  pages 406--420, 1992.

\bibitem{ipm:Karypis2}
G.~Karypis, A.~Gupta, and V.~Kumar.
\newblock A parallel formulation of interior point algorithms.
\newblock In {\em Proceedings Supercomputing\,'94 (Washington, D.C., USA,
  November 1994)}, pages 204--213. IEEE Computer Society, New York, NY, USA,
  1994.

\bibitem{ipm:Karypis1}
G.~Karypis, A.~Gupta, and V.~Kumar.
\newblock A highly parallel interior point algorithm.
\newblock {\em Proceedings of the 7th SIAM Conference on Parallel Processing
  for Scientific Computing}, pages 110--112, 1995.

\bibitem{ipm:Kas1}
P.~Kas, E.~Klafszky, L.~Malyusz, and G.~Izbirak.
\newblock Minimization of {Bregman's} divergence functions, and its relation to
  linear programming.
\newblock {Technical Report}, Department of Building Management and
  Organization, Technical University of Budapest, Muegyetem rkp.\,3, Budapest,
  1111~Hungary, 1998.

\bibitem{ipm:Kaeschel1}
J.~K{\"a}schel.
\newblock Karmarkar--{\"a}hnliche {Verfahren in der Linearen Optimierung
  (Karmarkar--type procedures in linear programming)}.
\newblock {Talk held at the DGOR--Jahrestagung in Stuttgart--Hohenheim,
  Germany}, Sektion Wirtschaftswissenschaften, TU Chemnitz, P.~O.~Box~964,
  D--9010~Chemnitz, East--Germany, September 1991.

\bibitem{ipm:Kaeschel2}
J.~K{\"a}schel.
\newblock {'' An efficient algorithm for linear programming '' of V. Ch.
  Venkaiah}.
\newblock {\em Proceedings of the Indian Academy of Sciences, Mathematical
  Sciences}, 102(2):155--158, 1992.
\newblock See also Venkaiah\,\cite{ipm:Venkaiah1}.

\bibitem{ipm:Katsura1}
R.~Katsura, M.~Fukushima, and T.~Ibaraki.
\newblock Interior methods for nonlinear minimum cost network flow problems.
\newblock {\em Journal of the Operations Research Society of Japan},
  32:174--179, 1989.

\bibitem{ipm:Kelly1}
T.~K. Kelly and J.~G. Ecker.
\newblock {EPM\,: An} exterior point method for linear programming.
\newblock {Technical Report}, April 1997.

\bibitem{ipm:Kennings1}
A.~A. Kennings, V.~H. Quintana, and A.~Vannelli.
\newblock Constraint matrix ordering for interior point algorithms on hypercube
  multiprocessors.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
  Symposium (Manhattan, KS, USA, September 1994)}, 1:187--195, 1994.

\bibitem{ipm:Kennings2}
A.~A. Kennings and A.~Vannelli.
\newblock An efficient interior point approach for {QP} and {LP} models of the
  relative placement problem.
\newblock {\em Proceedings of the 39th Midwest Symposium on Circuits and
  Systems}, 1/3:443--446, 1996.

\bibitem{ipm:Kennington1}
J.~L. Kennington.
\newblock Using {KORBX} for military airlift applications.
\newblock {\em Proceedings of the 28th IEEE Conference on Decision and
  Control}, pages 1603--1605, December 1989.

\bibitem{ipm:Keraghel1}
A.~Keraghel.
\newblock {\em Etude adaptive et comparative des prinicipales variantes dans
  l'algorithme de {Karmarkar}}.
\newblock PhD thesis, Laboratoire ARTEMIS (IMAG), Universite Joseph Fourier,
  BP~68, F--38402 St.~Martin d'Heres Cedex, France, 1989.
\newblock (In French).

\bibitem{ipm:Khachian1}
L.~G. Khachian and M.~J. Todd.
\newblock On the complexity of approximating the maximal inscribed ellipsoid
  for a polytope.
\newblock {Technical Report} 893, School of Operations Research and Industrial
  Engineering, College of Engineering, Cornell University, Ithaca,
  NY~14853--3801, USA, 1990.

\bibitem{ipm:Kim3}
K.~Kim.
\newblock {\em The effective integration of simplex and interior point
  techniques. {Part\,I\,: Decomposition, Part\,II\,: Null--space affine
  scaling}}.
\newblock PhD thesis, Department of Pure and Applied Mathematics, Washington
  State University, Pullman, WA~99164--3113, USA, 1991.
\newblock According to Part\,I see Kim and Nazareth \cite{ipm:Kim1}, for
  Part\,II see Kim and Nazareth \cite{ipm:Kim4}.

\bibitem{ipm:Kim1}
K.~Kim and J.~L. Nazareth.
\newblock The decomposition principle and algorithms for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:119--133, 1991.

\bibitem{ipm:Kim2}
K.~Kim and J.~L. Nazareth.
\newblock Implementation of a primal null--space affine scaling method and its
  extensions.
\newblock {Technical Report} 92--1, Department of Pure and Applied Mathematics,
  Washington State University, Pullman, WA~99164--3113, USA, January 1992.

\bibitem{ipm:Kim4}
K.~Kim and J.~L. Nazareth.
\newblock A primal null--space affine scaling method.
\newblock {\em ACM Transactions on Mathematical Software}, 20:373--392, 1994.

\bibitem{ipm:Kiwiel2}
K.~C. Kiwiel.
\newblock Complexity of some cutting plane methods that use analytic centers.
\newblock {\em Mathematical Programming}, 74:47--54, 1996.

\bibitem{ipm:Kiwiel1}
K.~C. Kiwiel.
\newblock Efficiency of the analytic center cutting plane method for convex
  minimization.
\newblock {\em SIAM Journal on Optimization}, 1996.

\bibitem{ipm:Klebor1}
S.~Klebor.
\newblock Interior point methods for large scale portfolio optimization.
\newblock Master's thesis, Institute of Mathematics, University of
  G{\"o}ttingen, G{\"o}ttingen, Germany, 1994.

\bibitem{ipm:Klerk9}
{E. de} Klerk.
\newblock {\em Interior point methods for semidefinite programming}.
\newblock PhD thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2600~GA~Delft, The Netherlands, 1997.

\bibitem{ipm:Klerk2}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock A nonconvex weighted potential function for polynomial target
  follwing methods.
\newblock {Technical Report} 95--127, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Klerk1}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Semi--definite problems in truss topology optimization.
\newblock {Technical Report} 95--128, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Klerk3}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Initialization in semidefinite programming via a self--dual
  skew--symmetric embedding.
\newblock {\em Opeartions Research Letters}, 20:213--221, 1997.

\bibitem{ipm:Klerk8}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Primal--dual potential reduction methods for semidefinite programming
  using affine--scaling directions.
\newblock {Technical Report} 97--29, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1997.

\bibitem{ipm:Klerk7}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock A short survey on semidefinite programming.
\newblock In W.~K. Klein~Haneveld et~al., editor, {\em {Ten Years LNMB, Ph.d.
  Research and Graduate Courses of the Dutch Network of Operations Research}},
  volume 122 of {\em CWI Tracts}, pages 323--339. Centrum for Mathematics and
  Informatics (CWI), Amsterdam, The Netherlands, 1997.

\bibitem{ipm:Klerk4}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Infeasible start semidefinite programming algorithms via self--dual
  embeddings.
\newblock In P.~M. Pardalos and H.~Wolkowicz, editors, {\em Topics in
  Semidefinite and Interior--Point Methods}, volume~18 of {\em Fields Institute
  Communications Series}, pages 215--236. American Mathematical Society (AMS),
  Providence, Rhode Island, USA, 1998.

\bibitem{ipm:Klerk5}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock On primal--dual path following algorithms for semidefinite
  programming.
\newblock In F.~Gianessi, S.~Koml{\'o}si, and T.~Rapcs{\'a}k, editors, {\em
  {New Trends in Mathematical Programming}}, pages 137--157. Kluwer Academic
  Publishers, Dordrecht, The Netherlands, 1998.

\bibitem{ipm:Klerk6}
{E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Polynomial primal--dual affine scaling algorithms in semidefinite
  programming.
\newblock {\em Journal of Combinatorial Optimization}, 2:51--69, 1998.

\bibitem{ipm:Kliokys1}
E.~Kliokys, E.~Handschin, and M.~Langer.
\newblock An interior point method for state elimination with current magnitude
  measurements and inequality constraints.
\newblock {\em Power Industry Computer Application Conference (Salt Lake City,
  UT, USA, 1995)}, pages 385--391, 1995.
\newblock See also Handschin et al. \cite{ipm:Handschin1}.

\bibitem{ipm:Knyazev1}
E.~A. Knyazev.
\newblock The method of centers with adaptation of parameters on the basis of
  the steepest descent.
\newblock {\em Issledovaniya po Prikladnoi Matematike (Kazanskii Universitet)},
  15:13--24, 1988.
\newblock (In Russian).

\bibitem{ipm:Koenker1}
R.~W. Koenker and B.-J. Park.
\newblock An interior point algorithm for nonlinear quantile regression.
\newblock {\em Journal of Econometrics}, 71:265--283, 1996.

\bibitem{ipm:Kojima1}
M.~Kojima.
\newblock Determining basic variables of optimal solutions in {Karmarkar's new
  LP} algorithm.
\newblock {\em Algorithmica}, 1(4):499--515, 1986.

\bibitem{ipm:Kojima30}
M.~Kojima.
\newblock A primitive interior--point algorithm for semidefinite programs in
  {Mathematica}.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--293, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, December 1994.

\bibitem{ipm:Kojima29}
M.~Kojima.
\newblock Basic lemmas in polynomial--time infeasible--interior--point methods
  for linear programs.
\newblock {\em Annals of Operations Research}, 62:1--28, 1996.

\bibitem{ipm:Kojima39}
M.~Kojima.
\newblock Semidefinite programming and interior--point methods.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--314, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, April
  1996.

\bibitem{ipm:Kojima22}
M.~Kojima and T.~Ishihara.
\newblock On the {$Big~M$} in the affine scaling algorithm.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--255, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, March 1992.

\bibitem{ipm:Kojima32}
M.~Kojima, S.~Kojima, and S.~Hara.
\newblock Linear algebra for semidefinite programming.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 1004:1--23,
  1997.

\bibitem{ipm:Kojima10}
M.~Kojima, Y.~Kurita, and S.~Mizuno.
\newblock Large--step interior point algorithms for linear complementarity
  problems.
\newblock {\em SIAM Journal on Optimization}, 3(2):398--412, 1993.

\bibitem{ipm:Kojima9}
M.~Kojima and N.~Megiddo.
\newblock The relation between the path of centers and {Smale's} regularization
  of the linear programming problem.
\newblock {\em Linear Algebra and Its Applications}, 152:135--139, 1991.

\bibitem{ipm:Kojima20}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A primal--dual exterior point algorithm for linear programming.
\newblock {Research Report} RJ~8500, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, December 1991.
\newblock See also Kojima, Megiddo and Mizuno\,\cite{ipm:Kojima27}.

\bibitem{ipm:Kojima43}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A {Lagrangian} relaxation method for approximating the analytic
  center of a polytope.
\newblock {Technical Report}, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1992.

\bibitem{ipm:Kojima11}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A general framework of continuation methods for complementarity
  problems.
\newblock {\em Mathematics of Operations Research}, 18:945--963, 1993.

\bibitem{ipm:Kojima27}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A primal--dual infeasible--interior--point algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 61:263--280, 1993.
\newblock See also Kojima, Megiddo and Mizuno\,\cite{ipm:Kojima20}.

\bibitem{ipm:Kojima12}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock Theoretical convergence of large--step--primal--dual interior point
  algorithms for linear programming.
\newblock {\em Mathematical Programming}, 59:1--21, 1993.

\bibitem{ipm:Kojima21}
M.~Kojima, N.~Megiddo, and S.~Mizuno.
\newblock A conjugate direction method for approximating the analytic center of
  a polytope.
\newblock {\em Journal of Inequalities and Applications}, 2:181--194, 1998.

\bibitem{ipm:Kojima34}
M.~Kojima, N.~Megiddo, S.~Mizuno, and S.~Shindoh.
\newblock Horizontal and vertical decomposition in interior point methods for
  linear programs.
\newblock {Research Report} RJ~9901, IBM Almaden Research Center, San Jose,
  CA~95120--6099, USA, 1994.

\bibitem{ipm:Kojima19}
M.~Kojima, N.~Megiddo, S.~Mizuno, and A.~Yoshise.
\newblock An artificial self--dual linear program.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Information Sciences, Tokyo Institute of Technology,
  Oh--Okayama, Meguro--ku, Tokyo~152, Japan, May 1992.
\newblock See Kojima et al.\ \cite{ipm:Kojima14}.

\bibitem{ipm:Kojima17}
M.~Kojima, N.~Megiddo, and T.~Noma.
\newblock Homotopy continuation methods for complementarity problems.
\newblock {Research Report} RJ~6638~(63949), IBM Almaden Research Center, San
  Jose, CA~95120--6099, USA, 1989.

\bibitem{ipm:Kojima18}
M.~Kojima, N.~Megiddo, and T.~Noma.
\newblock Homotopy continuation methods for nonlinear complementarity problems.
\newblock {\em Mathematics of Operations Research}, 16(4):754--774, 1991.

\bibitem{ipm:Kojima8}
M.~Kojima, N.~Megiddo, T.~Noma, and A.~Yoshise.
\newblock {\em {A Unified Approach to Interior Point Algorithms for Linear
  Complementarity Problems}}, volume 538 of {\em Lecture Notes in Computer
  Science}.
\newblock Springer Verlag, Berlin, Germany, 1991.

\bibitem{ipm:Kojima15}
M.~Kojima, N.~Megiddo, T.~Noma, and A.~Yoshise.
\newblock A unified approach to interior point algorithms for linear
  complementarity problems\,: {A} summary.
\newblock {\em Operations Research Letters}, 10:247--254, 1991.

\bibitem{ipm:Kojima3}
M.~Kojima, N.~Megiddo, and Y.~Ye.
\newblock An interior point potential reduction algorithm for the linear
  complementarity problem.
\newblock {\em Mathematical Programming}, 54:267--279, 1992.

\bibitem{ipm:Kojima13}
M.~Kojima, S.~Mizuno, and T.~Noma.
\newblock A new continuation method for complementarity problems with uniform
  {$P$}--functions.
\newblock {\em Mathematical Programming}, 43:107--113, 1989.

\bibitem{ipm:Kojima16}
M.~Kojima, S.~Mizuno, and T.~Noma.
\newblock Limiting behavior of trajectories by a continuation method for
  monotone complementarity problems.
\newblock {\em Mathematics of Operations Research}, 15(4):662--675, 1990.

\bibitem{ipm:Kojima24}
M.~Kojima, S.~Mizuno, and M.~J. Todd.
\newblock Infeasible--interior--point primal--dual potential--reduction
  algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:52--67, 1995.
\newblock See also Mizuno et al.\ \cite{ipm:Mizuno19}.

\bibitem{ipm:Kojima7}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A polynomial--time algorithm for a class of linear complementarity
  problems.
\newblock {\em Mathematical Programming}, 44:1--26, 1989.

\bibitem{ipm:Kojima4}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A primal--dual interior point algorithm for linear programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 29--47. Springer Verlag, New York,
  1989.

\bibitem{ipm:Kojima5}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock Ellipsoids that contain all the solutions of a positive
  semi--definite linear complementarity problems.
\newblock {\em Mathematical Programming}, 48:415--435, 1990.

\bibitem{ipm:Kojima6}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock An ${O(\sqrt{n}L)}$ iteration potential reduction algorithm for
  linear complementarity problems.
\newblock {\em Mathematical Programming}, 50:331--342, 1991.

\bibitem{ipm:Kojima26}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A convex property of monotone complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--267, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, March 1993.

\bibitem{ipm:Kojima14}
M.~Kojima, S.~Mizuno, and A.~Yoshise.
\newblock A little theorem of the {$Big-M$} in interior point algorithms.
\newblock {\em Mathematical Programming}, 59:361--375, 1993.

\bibitem{ipm:Kojima23}
M.~Kojima, T.~Noma, and M.~Satoh.
\newblock Potential reduction algorithms for monotone complementarity problems.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--251, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, 1992.

\bibitem{ipm:Kojima25}
M.~Kojima, T.~Noma, and A.~Yoshise.
\newblock Global convergence and detecting infeasibility in interior--point
  algorithms.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--257, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, September 1992.
\newblock See also Kojima, Noma and Yoshise \cite{ipm:Kojima28}.

\bibitem{ipm:Kojima28}
M.~Kojima, T.~Noma, and A.~Yoshise.
\newblock Global convergence in infeasible--interior--point algorithms.
\newblock {\em Mathematical Programming}, 65:43--72, 1994.
\newblock See also Kojima, Noma and Yoshise \cite{ipm:Kojima25}.

\bibitem{ipm:Kojima35}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Global and local convergence of predictor--corrector
  infeasible--interior--point algorithms for semidefinite programs.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--305, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, October 1995.

\bibitem{ipm:Kojima38}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock A note on the {Nesterov--Todd} and the {Kojima--Shindoh--Hara} search
  directions in semidefinite programming.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--313, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, April
  1996.

\bibitem{ipm:Kojima37}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock A predictor--corrector interior--point algorithm for the semidefinite
  linear complementarity problem using the {Alizadeh--Haeberly--Overton} search
  direction.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--311, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, January 1996.
\newblock To appear in {\em{SIAM Journal on Optimization}}.

\bibitem{ipm:Kojima31}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Reduction of monotone linear complementarity problems over cones to
  linear programs over cones.
\newblock {\em Acta Mathematica Vietnamica}, 22:147--157, 1997.

\bibitem{ipm:Kojima40}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Search directions in the {SDP} and the monotone {SDLCP}\,:
  {Generalization} and inexact computation.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--327, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March
  1997.

\bibitem{ipm:Kojima36}
M.~Kojima, M.~Shida, and S.~Shindoh.
\newblock Local convergence of predictor--corrector infeasible--interior--point
  algorithms for {SDP}s and {SDLCP}s.
\newblock {\em Mathematical Programming}, 80:129--160, 1998.

\bibitem{ipm:Kojima33}
M.~Kojima, S.~Shindoh, and S.~Hara.
\newblock Interior--point methods for the monotone semidefinite linear
  complementarity problem in symmetric matrices.
\newblock {\em SIAM Journal on Optimization}, 7:86--125, 1997.

\bibitem{ipm:Kojima2}
M.~Kojima and K.~Tone.
\newblock An efficient implementation of {Karmarkar's new LP} algorithm.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--180, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, 1986.

\bibitem{ipm:Kojima41}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Cones of matrices and successive convex relaxations of nonconvex
  sets.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--338, Department of Mathematical and Computing Sciences, Tokyo
  Institute of Technology, Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, March
  1998.

\bibitem{ipm:Kojima44}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Discretization and localization in successive convex relaxation
  methods for nonconvex quadratic optimization problems.
\newblock {Research Report} B--341, Department of Mathematical and Computing
  Sciences, Tokyo Institute of Technology, Oh--Okayama, Meguoro, Tokyo\,152,
  Japan, July 1998.
\newblock Also availble as\,: Technical Report COOR\,98--34, Department of
  Combinatorics and Optimization, University of Waterloo, Waterloo,
  Ontario\,N2L\,3G1, Canada.

\bibitem{ipm:Kojima42}
M.~Kojima and L.~Tun{\c{c}}el.
\newblock Monotonicity of primal-dual interior-point algorithms for
  semidefinite programming problems.
\newblock {\em Optimization Methods and Software}, 10:275--296, 1998.

\bibitem{ipm:Kolata1}
G.~Kolata.
\newblock A fast way to solve hard problems.
\newblock {\em Science}, 225:1379--1380, September 1984.

\bibitem{ipm:Konno2}
H.~Konno.
\newblock Recent advances in linear programming.
\newblock {\em Journal of the Japan Society of Simulation Technology},
  6(1):18--26, March 1987.
\newblock (In Japanese).

\bibitem{ipm:Konno1}
H.~Konno and Y.~Yajima.
\newblock Path--following algorithms for solving nonconvex programming
  problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Institute of Human and Social Science, Institute of Technology,
  2--12--1~Oh--Okayama, Meguro--ku, Tokyo\,152, Japan, October 1990.

\bibitem{ipm:Kortanek1}
K.~O. Kortanek.
\newblock Vector--supercomputer experiments with the linear programming scaling
  algorithm.
\newblock {Working Paper Series} 87--2, Department of Management Science,
  College of Business Administration, University of Iowa, Iowa City, IA~52240,
  USA, 1987.
\newblock See Kortanek and Zhu \cite{ipm:Kortanek13}, too.

\bibitem{ipm:Kortanek2}
K.~O. Kortanek.
\newblock A second order affine scaling algorithm for the geometric programming
  dual with logarithmic barrier.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Department
  of Management Science, College of Business Administration, University of
  Iowa, Iowa City, IA~52240, USA, August 1990.
\newblock See Kortanek and Ho \cite{ipm:Kortanek7}.

\bibitem{ipm:Kortanek13}
K.~O. Kortanek.
\newblock Vector--supercomputer experiments with the primal affine linear
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  University, New York, NY~10027, USA, October 1989.
\newblock See Goldfarb and Liu \cite{ipm:Goldfarb10}.

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\newblock {\em Proceedings of the CSI--91}, pages 433--439, 1991.

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\newblock A parallelisable block {Cholesky} factorization for staircase linear
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\newblock {CORE Discussion Paper} 9260, Center of Operations Research and
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\bibitem{ipm:Lu1}
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\newblock Network constrained security control using an interior point
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\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 8:1068--1076, 1993.

\bibitem{ipm:Lu2}
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\newblock A simplex--interior point algorithm for solving linear programming
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\newblock {\em Journal on Systems Science and Mathematical Sciences},
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\bibitem{ipm:Lu3}
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\newblock A generalized predictor--corrector linear programming algorithm.
\newblock {\em Mathematica Numerica Sinica}, 17:271--281, 1995.
\newblock (In Chinese, English summary).

\bibitem{ipm:Luo1}
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\newblock Parallel solution of the revised simplex method and interior point
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\newblock In {\em Proceedings of the 1991 International Symposium in Side,
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\bibitem{ipm:Luo6}
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\newblock Solving linear programming problems on transputers.
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\newblock Convergence analysis of a primal--dual interior point algorithm for
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\newblock {\em SIAM Journal on Optimization}, 7:697--716, 1997.

\bibitem{ipm:Luo11}
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\newblock Complexity analysis of a logarithmic barrier decomposition method for
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\newblock {Technical Report} 97--34, Faculty of Mathematics and Computer
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\newblock {\em SIAM Journal on Optimization}, 8:59--81, 1998.

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\newblock Cutting surfaces and analytic center\,: {A} polynomial algorithm for
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\newblock {Technical Report}, Economic Institute, Erasmus University Rotterdam,
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\newblock A modified predictor--corrector method for linear programming.
\newblock {\em Computational Optimization and Applications}, 3:83--91, 1994.

\bibitem{ipm:Luo14}
Z.-Q. Luo, S.-Q. Wu, and Y.~Ye.
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\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
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\newblock A genuine quadratically convergent polynomial interior point
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\newblock Optimization\,: {Methodolgy}, algorithms and applications.
\newblock {\em AT~\&~T Technical Journal}, 68:3--6, 1989.

\bibitem{ipm:Lustig1}
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\newblock A practical approach to {Karmarkar's} algorithm.
\newblock {Technical Report} SOL~85--5, Systems Optimization Laboratory,
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\bibitem{ipm:Lustig4}
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\newblock An experimental analysis of the convergence rate of an interior point
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\newblock {Technical Report} SOR~88--5, School of Engineering and Applied
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\bibitem{ipm:Lustig3}
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\newblock A generic primal--dual interior point algorithm.
\newblock {Technical Report} SOR~88--3, School of Engineering and Applied
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\bibitem{ipm:Lustig2}
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\newblock Identifying an optimal basis of a linear program using an interior
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
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\newblock An analysis of an available set of linear programming test problems.
\newblock {\em Computers and Operations Research}, 16:173--184, 1989.
\newblock Augmented version in the Technical Report SOL~87-11, Systems
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\bibitem{ipm:Lustig17}
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\newblock Phase\,1 search directions for a primal--dual interior point method
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\newblock Feasibility issues in aprimal--dual interior point method for linear
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\newblock {\em Mathematical Programming}, 49:145--162, 1990/91.

\bibitem{ipm:Lustig13}
I.~J. Lustig.
\newblock An implementation of a strongly polynomial time algorithm for basis
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\newblock {Technical Report} (in preparation), School of Engineering and
  Applied Science, Department of Civil Engineering and Operations Research,
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\bibitem{ipm:Lustig21}
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\newblock An implementation of a parallel primal--dual interior point method
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\newblock {\em Computational Optimization and Applications}, 1:141--161, 1992.

\bibitem{ipm:Lustig12}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock The primal--dual interior point method on the {C}ray supercomputer.
\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
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\bibitem{ipm:Lustig8}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Recent computational experience with the primal--dual interior point
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\newblock {Technical Report} RRR~46--89, RUTCOR Center of Operations Research,
  Rutgers University, New Brunswick, NJ~08903, USA, 1990.
\newblock Incorrect citation, elsewhere; see Lustig et al.\,\cite{ipm:Lustig7}.

\bibitem{ipm:Lustig15}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Starting and restarting the primal--dual interior point method.
\newblock {Technical Report} SOR~90--14, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1990.
\newblock Also available as\,: Rutgers Research Report 61--90, Rutgers
  University, New Brunswick, NJ, USA.

\bibitem{ipm:Lustig7}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Computational experience with a primal--dual interior point method
  for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:191--222, 1991.

\bibitem{ipm:Lustig18}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Interior method vs. simplex method\,: {Beyond {\tt netlib}}.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:41--44, August 1991.

\bibitem{ipm:Lustig11}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Recent advances in the {OB1} interior point code.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, School of Engineering and Applied Science, Department of
  Civil Engineering and Operations Research, Princeton University, Princeton,
  NJ~08544, USA, May 1991.
\newblock See Bixby et al.\ \cite{ipm:Bixby1}.

\bibitem{ipm:Lustig16}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock The interaction of algorithms and architectures for interior point
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\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
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\bibitem{ipm:Lustig14}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock On implementing {Mehrotra's} predictor--corrector interior point
  method for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:435--449, 1992.

\bibitem{ipm:Lustig19}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Computational experience with a globally convergent primal--dual
  predictor--corrector algorithm for linear programming.
\newblock {\em Mathematical Programming}, 66:123--135, 1994.

\bibitem{ipm:Lustig20}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock Interior point methods for linear programming\,: {Computational}
  state of the art.
\newblock {\em ORSA Journal on Computing}, 6:1--14, 1994.

\bibitem{ipm:Lustig22}
I.~J. Lustig, R.~E. Marsten, and D.~F. Shanno.
\newblock The last word on interior point methods for linear programming---for
  now.
\newblock {\em ORSA Journal on Computing}, 6:35--36, 1994.

\bibitem{ipm:Lustig9}
I.~J. Lustig, J.~M. Mulvey, and T.~J. Carpenter.
\newblock The formulation of stochastic programs for interior point methods.
\newblock {\em Operations Research}, 39(5):757--770, 1991.

\bibitem{ipm:Lustig23}
I.~J. Lustig and E.~Rothberg.
\newblock Gigaflops in linear programming.
\newblock {\em Operations Research Letters}, 18:157--165, 1996.

\bibitem{ipm:Lustig10}
I.~J. Lustig, D.~F. Shanno, and J.~W. Gregory.
\newblock The primal--dual interior point method on a {C}ray supercomputer.
\newblock {Technical Report} SOR~89--21, School of Engineering and Applied
  Science, Department of Civil Engineering and Operations Research, Princeton
  University, Princeton, NJ~08544, USA, 1989.
\newblock Same as Lustig et al.\ \cite{ipm:Lustig12}.

\bibitem{ipm:Luethi1}
H.-J. L{\"u}thi and B.~B{\"u}eler.
\newblock The analytic center quadratic cut method {(ACQCM)} for strongly
  monotone variational inequality problems.
\newblock {Technical Report}, Institute of Operations Research,
  Eidgen{\"o}ssische Technische Hochschule (ETH) Z{\"u}rich, Z{\"u}rich, The
  Switzerland, March 1998.

\bibitem{ipm:Ma1}
Z.~Ma.
\newblock On interior point algorithms for linear programming.
\newblock {\em Advanced Mathematics (Beijing, China)}, 21(3):274--288, 1992.
\newblock (In Chinese\,?).

\bibitem{ipm:Maaren1}
{H. van} Maaren and T.~Terlaky.
\newblock Inverse barriers and {CES}--functions in linear programming.
\newblock {\em Operations Research Letters}, 20, 1997.

\bibitem{ipm:Madrigal1}
M.~Madrigal and Q.~H. Quintana.
\newblock Optimal day--ahead network--constrained power system's market
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\newblock {\em Proceedings of the 11th Canadian Conference on Electrical and
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\bibitem{ipm:Mahony1}
R.~E. Mahony and J.~B. Moore.
\newblock Recursive interior--point linear programming algorithm based on
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\newblock In K.~H. Phua, C.~M. Wang, W.~Y. Yeong, T.~Y. Leong, H.~T. Loh, K.~C.
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S.~Maier.
\newblock {Primal--duales innere--Punkte--Verfahren mit endlicher Genauigkeit
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  finite accuracy for solving linear programs)}.
\newblock Master's thesis, Institut f{\"u}r Mathematik der
  Naturwissenschaftlichen Fakult{\"a}t der Universit{\"a}t Augsburg,
  D--8900~Augsburg, Germany, 1989.
\newblock (In German).

\bibitem{ipm:Man1}
H.~Man.
\newblock The effect of centering in an interior point algorithm.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2628~CD~Delft, The Netherlands, 1993.

\bibitem{ipm:Mangasarian1}
O.~L. Mangasarian and R.~Setiono.
\newblock Serial and parallel interior proximal point methods for linear
  programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Computer Science, University of Wisconsin, Madison,
  WI~53706, USA, May 1990.

\bibitem{ipm:Marcarenhas2}
W.~F. Marcarenhas.
\newblock New proofs of cobvergence for the dual affine scaling algorithm.
\newblock {Research Report}, Universidade Estadural de Campinas, Campinas~S.
  P., Brazil, 1993.

\bibitem{ipm:Marcarenhas1}
W.~F. Marcarenhas.
\newblock The affine scaling algorithm fails for stepsize 0.999.
\newblock {\em SIAM Journal on Optimization}, 7:34--46, 1997.

\bibitem{ipm:Margraff1}
G.~Margraff.
\newblock {Analyse und Modifikation des Karmarkar Verfahrens (Analysis and
  modification of Karmarkar's algorithm)}.
\newblock Master's thesis, Universit{\"a}t Trier, Fachbereich~IV,
  D--5500~Trier, Germany, 1987.
\newblock (In German).

\bibitem{ipm:Maros1}
I.~Maros and C.~M{\'e}sz{\'a}ros.
\newblock The role of the augmented system in interior point methods.
\newblock {\em European Journal of Operational Research}, 107:720--736, 1998.

\bibitem{ipm:Marsten7}
R.~E. Marsten.
\newblock The {IMP System} on personal computers.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
  USA}, Department of MIS, University of Arizona, Tucson, AZ~85721, USA,
  October 1987.

\bibitem{ipm:Marsten8}
R.~E. Marsten.
\newblock Interior point methods for large scale linear programming.
\newblock {Talk held at the Second International Conference on Industrial and
  Applied Mathematics (ICIAM~'91), Washington, DC, USA}, School of Industrial
  and Systems Engineering, Georgia Technology Institute, Atlanta,
  GA~30322--0205, USA, July 1991.

\bibitem{ipm:Marsten1}
R.~E. Marsten and M.~J. Saltzman.
\newblock A dual--affine interior point algorithm for {LP's} with bounded
  variables.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, Department of MIS, University of Arizona, Tucson, AZ~85721, USA,
  October 1988.
\newblock See Marsten et al.\ \cite{ipm:Marsten5}.

\bibitem{ipm:Marsten4}
R.~E. Marsten, M.~J. Saltzman, J.~W. Gregory, T.~G. Hewitt, and D.~F. Shanno.
\newblock The dual affine interior point method for linear programming
  implementation on {Cray} supercomputers.
\newblock {Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver,
  British Columbia, Canada}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30322--0205, USA, May 1989.

\bibitem{ipm:Marsten10}
R.~E. Marsten, M.~J. Saltzman, and D.~F. Shanno.
\newblock A dual affine interior point algorithm for {LP} with bounded
  varaibles.
\newblock {Talk held at the XIII International Symposium on Mathematical
  Programming in Tokyo, Japan}, School of Industrial and System Engineering,
  Georgia Institute of Technology, Atlanta, GA~30322, USA, August 1988.
\newblock See Marsten et al.\ \cite{ipm:Marsten5}.

\bibitem{ipm:Marsten5}
R.~E. Marsten, M.~J. Saltzman, D.~F. Shanno, J.~F. Ballintijn, and G.~S.
  Pierce.
\newblock Implementation of a dual affine interior point algorithm for linear
  programming.
\newblock {\em ORSA Journal on Computing}, 1:287--297, 1989.

\bibitem{ipm:Marsten2}
R.~E. Marsten and D.~F. Shanno.
\newblock On implementing {Karmarkar's} algorithm.
\newblock {Technical Report}, Department of MIS, University of Arizona, Tucson,
  AZ~85721, USA, 1985.
\newblock Same as Shanno and Marsten \cite{ipm:Shanno5}.

\bibitem{ipm:Marsten9}
R.~E. Marsten and D.~F. Shanno.
\newblock Interior point methods for linear programming\,: {Ready} for
  production use.
\newblock {Workshop at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, School of Industrial and System Engineering, Georgia Institute of
  Technology, Atlanta, GA~30322, USA, October 1990.

\bibitem{ipm:Marsten3}
R.~E. Marsten and D.~F. Shanno.
\newblock Recent computational experience with the primal--dual interior point
  method.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, School of Industrial and Systems Engineering, Georgia
  Technology Institute, Atlanta, GA~30322--0205, USA, January 1990.

\bibitem{ipm:Marsten11}
R.~E Marsten, D.~F. Shanno, and E.~M. Simantiraki.
\newblock Interior point methods for linear and nonlinear programming.
\newblock In I.~A. Duff and A.~Watson, editors, {\em Numerical Analysis\,: The
  State--of--the--Art}. Institute of Mathematics and its Applications, London,
  Great Britain, 1996.

\bibitem{ipm:Marsten6}
R.~E. Marsten, R.~Subramaniam, M.~J. Saltzman, I.~J. Lustig, and D.~F. Shanno.
\newblock Interior point methods for linear programming\,: {Just call Newton,
  Lagrange, and Fiacco and McCormick\,!}
\newblock {\em Interfaces}, 20(4):105--116, 1990.

\bibitem{ipm:Martinez1}
H.~J. Mart{\'i}nez.
\newblock On motivating the {Mitchell--Todd} modification of {Karmarkar's}
  algorithm for {LP} problems with free variables.
\newblock {\em Journal of Optimization Theory and Applications}, 84:675--679,
  1995.

\bibitem{ipm:Martinez2}
H.~J. Mart{\'i}nez, Z.~Parada, and R.~A. Tapia.
\newblock On the charactarization of {Q}--superlinear convergence of
  quasi--{Newton} interior--point methods for nonlinear programming.
\newblock {\em Boletin de la Sociedad Matematica Mexicana}, 1:137--148, 1995.

\bibitem{ipm:Martinhon1}
C.~Martinhon and C.~C. Gonzaga.
\newblock A unified analysis of affine and projective primal potential
  reduction algorithms for linear programming.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Systems Engineering and Computer Science,
  COPPE Federal University of Rio de Janeiro, 21941~Rio~de~Janeiro, RJ, Brazil,
  July 1991.

\bibitem{ipm:Marxen1}
A.~Marxen.
\newblock Primal barrier methods for linear programming.
\newblock {Technical Report} SOL~89--6, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, June 1989.

\bibitem{ipm:Marxen2}
A.~Marxen.
\newblock {\em Primal barrier methods for linear programming}.
\newblock PhD thesis, Systems Optimization Laboratory, Department of Operations
  Research, Stanford University, Stanford, CA~94305, USA, 1989.

\bibitem{ipm:Mascarenhas1}
W.~F. Mascarenhas.
\newblock The affine scaling algorithm fails for stepsize 0.999.
\newblock {\em SIAM Journal on Optimization}, 7:34--46, 1997.

\bibitem{ipm:Masuzawa1}
K.~Masuzawa, S.~Mizuno, and M.~Mori.
\newblock A polynomial time interior point algorithm for minimum cost flow
  problems.
\newblock {\em Journal of the Operations Research Society of Japan},
  33:157--167, 1990.

\bibitem{ipm:Matstoms1}
P.~Matstoms.
\newblock Sparse linear least squares problems in optimization.
\newblock {\em Computational Optimization and Applications}, 7:89--110, 1997.

\bibitem{ipm:McCormick1}
G.~P. McCormick.
\newblock Miscellaneous results concerning {Karmarkar's} projective method and
  {SUMT}.
\newblock {Manuscript} GWU/IMSE/Serial T--519/87, Institute for Management
  Science and Engineering, The George Washington University, Washington,
  D.C.~20052, USA, 1987.

\bibitem{ipm:McCormick3}
G.~P. McCormick.
\newblock The projective {SUMT} method for convex programming.
\newblock {\em Mathematics of Operations Research}, 14:203--223, 1989.

\bibitem{ipm:McCormick4}
G.~P. McCormick.
\newblock Resolving the {Shell Dual} with a nonlinear primal--dual algorithm.
\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
  Computing}, pages 233--246. North Holland, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:McCormick5}
G.~P. McCormick and A.~Sofer.
\newblock The {big--M} method for interior point feasibility in convex
  optimization.
\newblock {Technical Report} GWU/IMSE/Serial T--538/90, Institute for
  Management Science and Engineering, The George Washington University,
  Washington, D.C.~20052, USA, 1990.

\bibitem{ipm:McCormick2}
S.~T. McCormick and S.~F. Chang.
\newblock Making $aa{^T}$ sparser for interior--point algorithms\,:
  {Complexity} and heuristics.
\newblock {Technical Report}, Faculty of Commerce and Business Administration,
  University of British Columbia, Vancouver, BC~V6T\,1Y8, Canada, 1990.
\newblock In preparation.

\bibitem{ipm:McDiarmid2}
C.~McDiarmid.
\newblock Why {Karmarkar's} method is fast~?
\newblock {Talk held at the EURO/TIMS Joint International Conference on
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
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\newblock Implementation of affine scaling methods\,: {Towards} faster
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\newblock {Technical Report} 89--15, Department of Industrial Engineering and
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\newblock Higher order methods and their performance.
\newblock {Technical Report} TR~90--16R1, Department of Industrial Engineering
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\newblock Revised July 1991.

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\newblock {Technical Report} 91--13, Department of Industrial Engineering and
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\newblock Generalized prediction--corrector methods for solving linear
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
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\newblock Handling free variables in interior methods.
\newblock {Technical Report} 91--06, Department of Industrial Engineering and
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\newblock Higher--order methods for solving linear programs.
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\newblock On finding a vertex solution using interior point methods.
\newblock {\em Linear Algebra and Its Applications}, 152:233--253, 1991.

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\newblock Deferred rank--one updates in ${O(n^{3}L)}$ interior point algorithm.
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\newblock Implementation of affine scaling methods\,: {Approximate} solutions
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\newblock {\em ORSA Journal on Computing}, 4:103--118, 1992.

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\newblock On the implementation of a primal--dual interior point method.
\newblock {\em SIAM Journal on Optimization}, 2(4):575--601, 1992.

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S.~Mehrotra.
\newblock Quadratic convergence in a primal--dual method.
\newblock {\em Mathematics of Operations Research}, 18:741--751, 1993.

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\newblock Asymptotic convergence in a generalized predictor--corrector method.
\newblock {\em Mathematical Programming}, 74:11--28, 1996.

\bibitem{ipm:Mehrotra23}
S.~Mehrotra and R.~Fourer.
\newblock Solving symmetric indefinite systems in interior point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\bibitem{ipm:Mehrotra26}
S.~Mehrotra and R.~D.~C. Monteiro.
\newblock Parametric and range analysis for interior point methods.
\newblock {Technical Report}, Department of Systems and Industrial Engineering,
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\bibitem{ipm:Mehrotra29}
S.~Mehrotra and R.~A. Stubbs.
\newblock Predictor--corrector methods for a class of linear complementarity
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\newblock {\em SIAM Journal on Optimization}, 4:441--453, 1994.

\bibitem{ipm:Mehrotra14}
S.~Mehrotra and J.~Sun.
\newblock An algorithm for convex quadratic programming that requires
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\newblock {\em Mathematics of Operations Research}, 15:342--363, 1990.

\bibitem{ipm:Mehrotra12}
S.~Mehrotra and J.~Sun.
\newblock An interior point algorithm for solving smooth convex programs based
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\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\bibitem{ipm:Mehrotra15}
S.~Mehrotra and J.~Sun.
\newblock Path--following methods for convex programming.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
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\bibitem{ipm:Mehrotra11}
S.~Mehrotra and J.~Sun.
\newblock A method of analytic centers for quadratically constrained convex
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\newblock {\em SIAM Journal on Numerical Analysis}, 28(2):529--544, 1991.

\bibitem{ipm:Mehrotra13}
S.~Mehrotra and J.~Sun.
\newblock On computing the center of a quadratically constrained set.
\newblock {\em Mathematical Programming}, 50:81--89, 1991.

\bibitem{ipm:Mehrotra10}
S.~Mehrotra and J.~Sun.
\newblock On the implementation of a (primal--dual) interior point method.
\newblock {\em SIAM Journal on Optimization}, 2(4):575--601, 1992.

\bibitem{ipm:Mehrotra30}
S.~Mehrotra and J.-S. Wang.
\newblock Conjugate gradient based implementation of interior point methods for
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\newblock In L.~Adams and J.~L. Nazareth, editors, {\em Linear and Nonlinear
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\bibitem{ipm:Mehrotra21}
S.~Mehrotra and Y.~Ye.
\newblock On finding the optimal facet of linear programs.
\newblock {Technical Report} TR~91--10, Department of Industrial Engineering
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\newblock See also Mehrotra and Ye\,\cite{ipm:Mehrotra28}.

\bibitem{ipm:Mehrotra28}
S.~Mehrotra and Y.~Ye.
\newblock Finding an interior point in the optimal face of linear programs.
\newblock {\em Mathematical Programming}, 62:497--515, 1993.
\newblock See also Mehrotra and Ye\,\cite{ipm:Mehrotra21}.

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M.~S. Meketon.
\newblock Least absolute value regression.
\newblock {Working Paper}, AT~\&~T Bell Laboratories, Murray Hill, NJ~07974,
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M.~S. Meketon.
\newblock Optimization in simulation\,: {A} survey of recent results.
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\newblock Degeneracy issues in the affine scaling algorithm.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in St.~Louis,
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{J. C. O.} Mello, A.~C.~G. Melo, and S.~Granville.
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\newblock {\em IEEE Transaction on Power Systems}, 12:736--742, 1997.

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\newblock A new linesearch method for quadratically constrained convex
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\newblock {\em Operations Research Letters}, 16:67--77, 1994.

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A.~Melman.
\newblock A linesearch procedure in barrier methods for some convex programming
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\newblock {\em SIAM Journal on Optimization}, 6:283--298, 1996.

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A.~Melman and R.~Polyak.
\newblock Newton modified barrier function complexity for quadratic programming
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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A.~Melman and R.~Polyak.
\newblock The {Newton} modified barrier method for {QP} problems.
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\newblock {Primal--duale pfadorientierte Innere--{\"A}u{\ss}ere--Punkte--%
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  path--following interior--exterior--point methods for solving linear
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\newblock {Habilitationthesis}, Fachbereich Mathematik, Bergische
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\newblock (In German).

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\newblock Implementation of a first order central path following algorithm for
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\newblock {Technical Report} 202, Institut f{\"u}r Angewandte Mathematik und
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\newblock {\em Mise en oeuvre et developpements de la methode de plans coupants
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\newblock PhD thesis, Department of Management Studies, University of Geneva,
  CH--1211 Geneva, Switzerland, 1995.
\newblock (In French).

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M.~Mesbahi and G.~P. Papavassilopoulos.
\newblock {LMIs}, interior point methods, complexity theory, and robust
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\newblock {\em Proceedings of the 35th IEEE conference on Decision and
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\newblock On the modifications of the affine scaling algorithm for linear
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\newblock {\em Alkamazott Matematikai Lapok}, 17:185--194, 1993.
\newblock (In Hungarian, English summary).

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C.~M{\'e}sz{\'a}ros.
\newblock The {''inexact''} minimum local fill--in ordering algorithm.
\newblock {Working Paper} WP 95--7, Computer and Automation Research Institute,
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\newblock Submitted to {\em{ACM Transactions on Mathematical Software}}.

\bibitem{ipm:Meszaros7}
C.~M{\'e}sz{\'a}ros.
\newblock {\em The efficient implementation of interior point methods for
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\newblock PhD thesis, E{\"o}tv{\"o}s Lor{\'a}nd University of Sciences,
  Budapest, Hungary, 1996.

\bibitem{ipm:Meszaros4}
C.~M{\'e}sz{\'a}ros.
\newblock Fast {Cholesky} factorization of interior point methods of linear
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\newblock {\em Computers and Mathematics with Applications}, 31:49--54, 1996.

\bibitem{ipm:Meszaros3}
C.~M{\'e}sz{\'a}ros.
\newblock The augmented system variant of {IPM}s in two--stage stochastic
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\newblock {\em European Journal of Operational Research}, 101:317--327, 1997.

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C.~M{\'e}sz{\'a}ros.
\newblock Steplengths in infeasible primal--dual interior point algorithms for
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\newblock {Technical Report} DOC~97/7, Imperial College, London, United
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C.~M{\'e}sz{\'a}ros.
\newblock On aproperty of the {Cholesky} factorization and its consequences in
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\newblock {Working Paper} WP\,98--7, Laboratory of Operations Research and
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C.~M{\'e}sz{\'a}ros.
\newblock On free variables in interior point methods.
\newblock {\em Optimization Methods and Software}, 9:121--139, 1998.

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C.~M{\'e}sz{\'a}ros.
\newblock On the sparsity issues of interior point methods for quadratic
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\newblock {Working Paper} WP\,98--4, Laboratory of Operations Research and
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\newblock The separable and non--separable formulations of convex quadratic
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\newblock {Working Paper} WP\,98--3, Laboratory of Operations Research and
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R.~R. Meyer and G.~L. Schultz.
\newblock Structured interior point methods for multicommodity flows.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
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S.~Miagen and T.~Miyazaki.
\newblock Implementation and numerical experiments on an interior--point
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\newblock In {\em Proceedings of the InfoJapan~'90\ : Information Technology
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\newblock A quadratically convergent {$O((1 + \kappa)\sqrt{n}L)$}-- iteration
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\newblock {Research Report} RRR~93--93, RUTCOR\,--\,Rutgers Center for
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\newblock Two infeasible interior--point predictor--corrector algorithms for
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\newblock {\em SIAM Journal on OPtimization}, 6:587--599, 1996.

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\newblock New suggested implementation of {Karmarkar's} algorithm.
\newblock Cahier~71, Laboratoire de Analyse et Modelisation de Systemes pour
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\newblock Towards a probabilistic analysis of {Karmarkar's} algorithm.
\newblock Cahier, Laboratoire de Analyse et Modelisation de Systemes pour
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\newblock Probabilistic bounds on one step objective/potential function
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\newblock {\em R.A.I.R.O Recherche Operationnelle/Operations Research},
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J.~E. Mitchell.
\newblock {\em Karmarkar's algorithm and combinatorial optimization problems}.
\newblock PhD thesis, School of Operations Research and Industrial Engineering,
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J.~E. Mitchell.
\newblock An interior point column generation method for linear programming
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
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\bibitem{ipm:Mitchell11}
J.~E. Mitchell.
\newblock Updating lower bounds when using {Karmarkar's} projective algorithm
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\newblock {\em Journal of Optimization Theory and Applications}, 78:127--142,
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\bibitem{ipm:Mitchell8}
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\newblock An interior point column generation method for linear programming
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\newblock {\em SIAM Journal on Optimization}, 4:423--440, 1994.

\bibitem{ipm:Mitchell19}
J.~E. Mitchell.
\newblock Interior point methods for combinatorial optimization.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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J.~E. Mitchell.
\newblock Interior point methods for integer programming.
\newblock In J.~E. Beasley, editor, {\em {Advances in Linear and Integer
  Programming}}, volume~4 of {\em Oxford Lecture Series in Mathematics and its
  Applications}, pages 223--248. Oxford Science Publications, Oxford University
  Press, Oxford, Great Britain, 1996.

\bibitem{ipm:Mitchell20}
J.~E. Mitchell.
\newblock Computational experience with an interior point cutting plane
  algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, February 1997.
\newblock Revised April 1997.

\bibitem{ipm:Mitchell18}
J.~E. Mitchell.
\newblock Fixing variables and generating classical cutting planes when using
  an interior branch and cut method to solve integer programming problems.
\newblock {\em European Journal of Operational Research}, 97:139--148, 1997.

\bibitem{ipm:Mitchell21}
J.~E. Mitchell.
\newblock An interior point cutting plane algorithm for {Ising}spin glass
  problems.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, July 1997.
\newblock Revised April 1997.

\bibitem{ipm:Mitchell14}
J.~E. Mitchell and B.~Borchers.
\newblock A primal--dual interior point cutting plane method for the linear
  ordering problem.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Bulletin}, 21:13--18, 1992.

\bibitem{ipm:Mitchell15}
J.~E. Mitchell and B.~Borchers.
\newblock Solving real--world linear ordering problems using a primal--dual
  interior point cutting plane method.
\newblock {\em Annals of Operatiomns Research}, 62:253--276, 1996.

\bibitem{ipm:Mitchell22}
J.~E. Mitchell and B.~Borchers.
\newblock Solving linear ordering problems with a combined interior
  point/simplex cutting plane algorithm.
\newblock {Technical Report}, Department of Mathematical Sciences, Rensselaer
  Polytechnic Institute, Troy, NY~12180--3590, USA, September 1997.

\bibitem{ipm:Mitchell23}
J.~E. Mitchell, P.~M. Pardalos, and M.~G.~C. Resende.
\newblock Interior point methods for combinatorial optimization.
\newblock In D.-Z. Du and P.~M. Pardalos, editors, {\em Handbook of
  Combinatorial Optimization}, pages 189--298. Kluwer Academic Publishers,
  Dordrecht, The Netherlands, 1998.
\newblock See also Mitchell\,\cite{ipm:Mitchell19}.

\bibitem{ipm:Mitchell17}
J.~E. Mitchell and S.~Ramaswamy.
\newblock A long--step, cutting plane algorithm for linear and convex
  programming.
\newblock {Technical Report} 37--93--387, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, August 1993.
\newblock Title before August 1994 revision\,: {An extension of Atkinson and
  Vaidya's algorithm that uses central trajectory}.

\bibitem{ipm:Mitchell12}
J.~E. Mitchell and M.~J. Todd.
\newblock Two variants of {Karmarkar's} linear programming algorithm for
  problems with some unrestricted variables.
\newblock {Technical Report} 741, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--7501, USA, 1987.
\newblock Incorporated in Mitchell and Todd \cite{ipm:Mitchell4}.

\bibitem{ipm:Mitchell3}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving linear ordering problems using {Karmarkar's} algorithm.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--7501, USA, 1988.
\newblock Incorrect citation, elsewhere; part of Mitchell \cite{ipm:Mitchell1},
  and of Mitchell and Todd \cite{ipm:Mitchell6}.

\bibitem{ipm:Mitchell2}
J.~E. Mitchell and M.~J. Todd.
\newblock On the relationship between the search directions in the affine and
  projective variants of {Karmarkar's} linear programming algorithm.
\newblock In B.~Cornet and H.~Tulkens, editors, {\em Contributions to
  Operations Research and Economics\,: The Twentieth Anniversary of CORE},
  pages 237--250. M.I.T. Press, Cambridge, MA, USA, 1989.

\bibitem{ipm:Mitchell5}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
  algorithm, {Part\,I\,: Theory}.
\newblock {RPI Technical Report} 172, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, January 1989.

\bibitem{ipm:Mitchell6}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
  algorithm, {Part\,II\,: Computational} results.
\newblock {RPI Technical Report} 173, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, January 1989.

\bibitem{ipm:Mitchell7}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving perfect matching problems using {Karmarkar's} algorithm.
\newblock {RPI Technical Report} 174, Department of Mathematical Sciences,
  Rensselaer Polytechnic Institute, Troy, NY~12180--3590, USA, August 1989.
\newblock See Mitchell and Todd \cite{ipm:Mitchell10}, too.

\bibitem{ipm:Mitchell4}
J.~E. Mitchell and M.~J. Todd.
\newblock A variant of {Karmarkar's} linear programming algorithm for problems
  with some unrestricted variables.
\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 10:30--38,
  1989.

\bibitem{ipm:Mitchell10}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving perfect matching problems using {Karmarkar's} algorithm.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 309--318. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Mitchell9}
J.~E. Mitchell and M.~J. Todd.
\newblock Solving combinatorial optimization problems using {Karmarkar's}
  algorithm.
\newblock {\em Mathematical Programming}, 56:245--284, 1992.
\newblock Combination and shortening of Mitchell and Todd
  \cite{ipm:Mitchell5,ipm:Mitchell6}.

\bibitem{ipm:Mitra3}
G.~Mitra and R.~Levkovitz.
\newblock {\em {Interior Point Methods for Linear Programming Optimization\,:
  Theory and Practice}}.
\newblock John Wiley\,\&\,Sons, New York, USA, 1997.

\bibitem{ipm:Mitra2}
G.~Mitra, M.~Tamiz, and J.~Yadegar.
\newblock Experimental investigation of an interior search method within a
  simplex framework.
\newblock {\em Communications of the ACM}, 31(12):1474--1482, 1988.

\bibitem{ipm:Mitra1}
G.~Mitra, M.~Tamiz, and J.~Yadegar.
\newblock A hybrid algorithm for linear programming.
\newblock In A.~J. Osiadacz, editor, {\em Simulation and Optimization of Large
  Systems}, volume~13 of {\em The Institute of Mathematics and Its Applications
  Conference Series}, pages 143--159. Clarendon Press, Oxford, England, 1988.

\bibitem{ipm:Mizuno1}
S.~Mizuno.
\newblock An ${O(n^{3}L)}$ algorithm using a sequence for linear
  complementarity problems.
\newblock {\em Journal of the Operations Research Society of Japan}, 33:66--75,
  1990.

\bibitem{ipm:Mizuno2}
S.~Mizuno.
\newblock A rank--one updating interior algorithm for linear programming.
\newblock {\em Arabian Journal for Science and Engineering}, 15(4):671--677,
  1990.

\bibitem{ipm:Mizuno10}
S.~Mizuno.
\newblock {$O(n^{\rho}L)$} iteration {$O(n^{3}L)$} potential reduction
  algorithms for linear programming.
\newblock {\em Linear Algebra and Its Applications}, 152:155--168, 1991.

\bibitem{ipm:Mizuno9}
S.~Mizuno.
\newblock A new polynomial time method for a linear complementarity problem.
\newblock {\em Mathematical Programming}, 56:31--43, 1992.

\bibitem{ipm:Mizuno16}
S.~Mizuno.
\newblock Polynomiality of the {Kojima--Megiddo--Mizuno} infeasible interior
  point algorithm for linear programming.
\newblock {Technical Report} 1006, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, May 1992.
\newblock See also Mizuno \cite{ipm:Mizuno21}.

\bibitem{ipm:Mizuno17}
S.~Mizuno.
\newblock A primal--dual interior point method for linear programming.
\newblock {Research Reports on Information Sciences, Ser.\,B\,: Operations
  Research} B--252, Department of Information Sciences, Tokyo Institute of
  Technology, Oh--Okayama, Meguro--ku, Tokyo~152, Japan, January 1992.
\newblock (In Japanese).

\bibitem{ipm:Mizuno21}
S.~Mizuno.
\newblock Polynomiality of infeasible interior--point algorithms for linear
  programming.
\newblock {\em Mathematical Programming}, 67:109--119, 1994.
\newblock See also Mizuno \cite{ipm:Mizuno16}.

\bibitem{ipm:Mizuno22}
S.~Mizuno.
\newblock A predictor--corrector infeasible--interior--point algorithm for
  linear programming.
\newblock {\em Operations Research Letters}, 16:61--66, 1994.

\bibitem{ipm:Mizuno24}
S.~Mizuno.
\newblock Research in interior--point methods.
\newblock {\em Proceedings of the Institute of Statistical Mathematics (Tokyo,
  Japan)}, 42:103--109, 1994.
\newblock (In Japanese).

\bibitem{ipm:Mizuno27}
S.~Mizuno.
\newblock Infeasible--interior--point algorithms.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 159--187. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Mizuno25}
S.~Mizuno.
\newblock A superlinearly convergent infeasible--interior--point algorithm for
  geometrical {LCPs} without a strictly complementarity condition.
\newblock {\em Mathematics of Operations Research}, 21:382--400, 1996.

\bibitem{ipm:Mizuno23}
S.~Mizuno and F.~Jarre.
\newblock An infeasible--interior--point algorithm using projections onto a
  convex set.
\newblock {\em Annals of Operations Research}, 62:59--80, 1993.
\newblock See also Mizuno and Jarre \cite{ipm:Jarre18}.

\bibitem{ipm:Mizuno29}
S.~Mizuno and F.~Jarre.
\newblock Global and polynomial--time convergence of an
  infeasible--interior--point algorithm using inexact computation.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku}, 981:22--35,
  1997.
\newblock See also Mizuno and Jarre\,\cite{ipm:Mizuno31}.

\bibitem{ipm:Mizuno31}
S.~Mizuno and F.~Jarre.
\newblock Global and polynomial--time convergence of an
  infeasible--interior--point algorithm using inexact computation.
\newblock {\em Mathematical Programming}, 84:39--53, 1999.
\newblock See also Mizuno and Jarre\,\cite{ipm:Mizuno29}.

\bibitem{ipm:Mizuno26}
S.~Mizuno, F.~Jarre, and J.~Stoer.
\newblock A unified approach to infeasible--interior--point algorithms via
  geometrical linear complementarity problems.
\newblock {\em Applied Mathematics\,\&\,Optimization}, 33:315--341, 1996.

\bibitem{ipm:Mizuno19}
S.~Mizuno, M.~Kojima, and M.~J. Todd.
\newblock Infeasible--interior--point primal--dual potential--reduction
  algorithms for linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:52--67, 1995.

\bibitem{ipm:Mizuno3}
S.~Mizuno and K.~Masuzawa.
\newblock Polynomial time interior point algorithms for transportation
  problems.
\newblock {\em Journal of the Operations Research Society of Japan},
  32:371--382, 1989.

\bibitem{ipm:Mizuno28}
S.~Mizuno, N.~Megiddo, and T.~Tsuchiya.
\newblock A linear programming instance with many crossover events.
\newblock {\em Journal of Complexity}, 12:474--479, 1996.

\bibitem{ipm:Mizuno14}
S.~Mizuno and A.~Nagasawa.
\newblock Strict monotonicity in {Todd's} low--complexity algorithm for linear
  programming.
\newblock {\em Operations Research Letters}, 12:59--64, 1992.

\bibitem{ipm:Mizuno15}
S.~Mizuno and A.~Nagasawa.
\newblock A primal--dual affine scaling potential reduction algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 62:119--131, 1993.

\bibitem{ipm:Mizuno13}
S.~Mizuno, R.~Saigal, and J.~B. Orlin.
\newblock Determination of optimal vertices from feasible solution in
  unimodular programming.
\newblock {\em Mathematical Programming}, 59:23--31, 1993.

\bibitem{ipm:Mizuno11}
S.~Mizuno and M.~J. Todd.
\newblock An {$O(n^{3}L)$} long step path following algorithm for a linear
  complementarity problem.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1989.
\newblock Same as Mizuno and Todd \cite{ipm:Mizuno12}.

\bibitem{ipm:Mizuno12}
S.~Mizuno and M.~J. Todd.
\newblock An {$O(n^{3}L)$} adaptive path following algorithm for a linear
  complementarity problem.
\newblock {\em Mathematical Programming}, 52:587--595, 1991.

\bibitem{ipm:Mizuno30}
S.~Mizuno and M.~J. Todd.
\newblock On two homogeneous self--dual systems for linear programming and its
  extensions.
\newblock {Research Memorandum} 687, The Institute of Statistical Mathematics,
  4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, 1998.
\newblock Also issued as {Technical Report No.\,1213, School of Operations
  Research and Industrial Engineering, Cornell University, Ithaca,
  NY~14853--3801, USA}.

\bibitem{ipm:Mizuno18}
S.~Mizuno, M.~J. Todd, and L.~Tun{\c c}el.
\newblock Monotonicity of primal and dual objective values in primal--dual
  interior--point algorithms.
\newblock {\em SIAM Journal on Optimization}, 4:613--625, 1994.

\bibitem{ipm:Mizuno4}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of path--following algorithms for linear
  programming.
\newblock {Technical Report} 878, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1989.
\newblock See Mizuno et al.\ \cite{ipm:Mizuno8}.

\bibitem{ipm:Mizuno6}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of interior point algorithms for linear
  programming.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1990.
\newblock Incorrect citation, elsewhere.

\bibitem{ipm:Mizuno5}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock Anticipated behavior of long--step algorithms for linear programming.
\newblock {Technical Report} 882, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1990.
\newblock Also available as {\em Technical Report 24, Department of Management
  Science and Engineering, Tokyo Institute of Technology, Oh--Okayama,
  Meguro--ku, Tokyo~152, Japan, 1989} and {\em Technical Report 89--23,
  Department of Management Science, University of Iowa, Iowa City, IA~52242,
  USA, 1989}. See also Mizuno et al.\, \cite{ipm:Mizuno8}.

\bibitem{ipm:Mizuno8}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock On adaptive--step primal--dual interior--point algorithms for linear
  programming.
\newblock {\em Mathematics of Operations Research}, 18:964--981, 1993.
\newblock Revised and combined version of Mizuno et al.\,
  \cite{ipm:Mizuno4,ipm:Mizuno5}.

\bibitem{ipm:Mizuno20}
S.~Mizuno, M.~J. Todd, and Y.~Ye.
\newblock A surface of analytic centers and infeasible--interior--point
  algorithms for linear programming.
\newblock {\em Mathematics of Operations Research}, 20:135--162, 1995.

\bibitem{ipm:Mizuno7}
S.~Mizuno, A.~Yoshise, and T.~Kikuchi.
\newblock Practical polynomial time algorithms for linear complementarity
  problems.
\newblock {\em Journal of the Operations Research Society of Japan}, 32:75--92,
  1989.

\bibitem{ipm:Momoh7}
J.~A. Momoh, R.~F. Austin, R.~Adapa, and E.~C. Ogbuobiri.
\newblock Application of interior point method to economic dispatch.
\newblock {\em Proceedings of the IEEE International Conference on Systems, Man
  and Cybernetics (Chicago, IL, USA, October 1992)}, 2:1096--1101, 1993.

\bibitem{ipm:Momoh4}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock Evaluation of interior point methods and their application to power
  systems economic dispatch.
\newblock {\em Proceedings of the 1993 North American Power Symposium
  (Washington, D.C., USA, October 1993)}, pages 116--123, 1994.

\bibitem{ipm:Momoh2}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock Rule based support for partioning networks for optimal power flows.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
  Symposium (Manhattan, KS, USA, September 1994)}, 1:376--381, 1994.

\bibitem{ipm:Momoh5}
J.~A. Momoh, G.~F. Brown, and R.~Adapa.
\newblock {VAr} planning using partitioned power system networks.
\newblock {\em Proceedings of the 36th Midwest Symposium on Circuits and
  Systems (Detroit, MI, USA, August 1993)}, 1:372--376, 1994.

\bibitem{ipm:Momoh3}
J.~A. Momoh and S.~X. Guo.
\newblock An enhanced quadratic interior point method to solve power system
  {VAr} planning.
\newblock {\em Proceedings of the 1993 North American Power Symposium
  (Washington, D.C., USA, October 1993)}, pages 215--221, 1994.

\bibitem{ipm:Momoh1}
J.~A. Momoh, S.~X. Guo, E.~C. Ogbuobiri, and R.~Adapa.
\newblock The quadratic interior point method solving power system optimization
  problems.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:1327--1336, 1994.
\newblock See also\,: {\em IEEE International Conference on Systems, Man and
  Cybernetics 1\,(1992), 1096--}.

\bibitem{ipm:Momoh6}
J.~A. Momoh, P.~J. Lusaka, R.~Adapa, and E.~C. Ogbuobiri.
\newblock Heurstic--based algorithms for enhanced interior point based {OPF}.
\newblock {\em Expert System Application to Power Systems (Proceedings of the
  January 1993 Melbourne Conference)}, IV:686--696, 1994.

\bibitem{ipm:Monma1}
C.~L. Monma.
\newblock Recent breakthroughs in linear programming methods.
\newblock {Internal Memorandum}, Bell Communications Research, Morristown,
  NJ~07960, USA, 1987.

\bibitem{ipm:Monma2}
C.~L. Monma.
\newblock Successful implementations of interior algorithms.
\newblock {\em SIAM News}, 22(2):14--16, March 1989.

\bibitem{ipm:Monma3}
C.~L. Monma and A.~J. Morton.
\newblock Computational experience with the dual affine variant of
  {Karmarkar's} method for linear programming.
\newblock {\em Operations Research Letters}, 6:261--267, 1987.

\bibitem{ipm:Monteiro9}
R.~D.~C. Monteiro.
\newblock Convergence and boundary behavior of the projective scaling
  trajectories for linear programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 213--229. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Monteiro10}
R.~D.~C. Monteiro.
\newblock Convergence and boundary behavior of the projective scaling
  trajectories for linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):842--858, 1991.

\bibitem{ipm:Monteiro13}
R.~D.~C. Monteiro.
\newblock The global convergence of a class of primal potential reduction
  algorithms for convex programming.
\newblock {Technical Report}, Department of Systems and Industrial Engineering,
  University of Arizona, Tucson, AZ~85721, USA, August 1991.

\bibitem{ipm:Monteiro8}
R.~D.~C. Monteiro.
\newblock An implementation of range analysis for {LP} problems solved via
  interior point methods.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Department of Systems and Industrial Engineering,
  University of Arizona, Tucson, AZ~85721, USA, July 1991.

\bibitem{ipm:Monteiro1}
R.~D.~C. Monteiro.
\newblock On the continuous trajectories for a potential reduction algorithm
  for linear programming.
\newblock {\em Mathematics of Operations Research}, 17:225--253, 1992.

\bibitem{ipm:Monteiro11}
R.~D.~C. Monteiro.
\newblock A globally convergent primal--dual interior point algorithm for
  convex programming.
\newblock {\em Mathematical Programmingh}, 64:123--147, 1994.

\bibitem{ipm:Monteiro24}
R.~D.~C. Monteiro.
\newblock Primal--dual algorithms for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 7:663--678, 1997.
\newblock Former technical report title (Oct. 1995)\,: Primal--dual
  path--following algorithms for semidefinite programming.

\bibitem{ipm:Monteiro32}
R.~D.~C. Monteiro.
\newblock Polynomial convergence of primal--dual algorithms for semidefinite
  programming based on {Monteiro and Zhang} family of directions.
\newblock {\em SIAM Journal on Optimization}, 8:797--812, 1998.

\bibitem{ipm:Monteiro2}
R.~D.~C. Monteiro and I.~Adler.
\newblock An ${O(n^{3}L)}$ primal--dual interior point algorithm for linear
  programming.
\newblock {Technical Report} ORC~87--4, Department of Industrial Engineering
  and Operations Research, University of California, Berkeley, CA~94720, USA,
  1987.

\bibitem{ipm:Monteiro6}
R.~D.~C. Monteiro and I.~Adler.
\newblock A polynomial primal--dual affine algorithm for {LP}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Denver, CO,
  USA}, Engineering Systems Research Center, University of California,
  Berkeley, CA~94720, USA, October 1988.

\bibitem{ipm:Monteiro3}
R.~D.~C. Monteiro and I.~Adler.
\newblock Interior path following primal--dual algorithms\,: {Part\,I\,:
  Linear} programming.
\newblock {\em Mathematical Programming}, 44:27--41, 1989.

\bibitem{ipm:Monteiro4}
R.~D.~C. Monteiro and I.~Adler.
\newblock Interior path following primal--dual algorithms\,: {Part\,II\,:
  Convex} quadratic programming.
\newblock {\em Mathematical Programming}, 44:43--66, 1989.

\bibitem{ipm:Monteiro5}
R.~D.~C. Monteiro and I.~Adler.
\newblock An extension of {Karmarkar--type} algorithm to a class of convex
  separable programming problems with global linear rate of convergence.
\newblock {\em Mathematics of Operations Research}, 15:408--422, 1990.

\bibitem{ipm:Monteiro7}
R.~D.~C. Monteiro, I.~Adler, and M.~G.~C. Resende.
\newblock A polynomial--time primal--dual affine scaling algorithm for linear
  and convex quadratic programming and its power series extension.
\newblock {\em Mathematics of Operations Research}, 15:191--214, 1990.

\bibitem{ipm:Monteiro25}
R.~D.~C. Monteiro and S.~Mehrotra.
\newblock A general parametric analysis approach and its implication to
  sensitivity analysis in interior point methods.
\newblock {\em Mathematical Programming}, 72:65--82, 1996.

\bibitem{ipm:Monteiro26}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock Properties of an interior--point mapping for mixed complementarity
  problems.
\newblock {\em Mathematics of Operations Research}, 21:629--654, 1996.

\bibitem{ipm:Monteiro29}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock A potential reduction {Newton} method for constrained equations.
\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30322--0205, USA, March 1997.

\bibitem{ipm:Monteiro35}
R.~D.~C. Monteiro and J.-S. Pang.
\newblock On two interior--point mappings for nonlinear semidefinite
  complementarity problems.
\newblock {\em Mathematics of Operations Research}, 23:39--60, 1998.

\bibitem{ipm:Monteiro15}
R.~D.~C. Monteiro, J.-S. Pang, and T.~Wang.
\newblock A positive algorithm for the nonlinear complementarity problem.
\newblock {\em SIAM Journal on Optimization}, 5:129--148, 1995.

\bibitem{ipm:Monteiro14}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Limiting behavior of the derivatives of certain trajectories
  associated with a monotone horizontal linear complementarity problem.
\newblock {\em Mathematics of Operations Research}, 21:793--814, 1996.

\bibitem{ipm:Monteiro30}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomial convergence of a new family of primal--dual algorithms for
  semidefinite programming.
\newblock {Research Memorandum} 627, The Institute of Statistical Mathematics,
  4--6--7 Minami--Azabu, Minato--Ku, Tokyo~106, Japan, 1996.

\bibitem{ipm:Monteiro31}
R.~D.~C. Monteiro and T.~Tsuchiya.
\newblock Polynomiality of primal--dual algorithms for semidefinite linear
  complementarity problems based on the {Kojima--Shindoh--Hara} family of
  directions.
\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku},
  1004:138--152, 1997.
\newblock See also Monteiro and Tsuchiya\,\cite{ipm:Monteiro38}.

\bibitem{ipm:Monteiro21}
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\newblock {\em SIAM Journal on Optimization}, 8:26--58, 1998.

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\newblock {Technical Report}, School of Industrial and Systems Engineering,
  Georgia Technology Institute, Atlanta, GA~30338, USA, May 1998.

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\newblock {\em Annals of Operations Research}, 46/47:443--482, 1993.

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\newblock {Technical Report} 92--13, Department of Systems and Industrial
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\newblock Also available as {\em Technical Report MSC--P316--0792, Mathematical
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\newblock Linear programming made simpler than simplex.
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\newblock Approximate projections for the {Karmarkar} algorithm.
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R.~Polyak.
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R.~Polyak.
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R.~Polyak.
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\newblock In {\em Proceedings of the Air Force/NASA Symposium on Recent
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\bibitem{ipm:Polyak13}
R.~Polyak.
\newblock Nonlinear rescaling principle in constrained optimization.
\newblock {Talk held at the International Congress of Mathematicians in Kyoto,
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\bibitem{ipm:Polyak14}
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\newblock Interior augmented lagrangians.
\newblock {Talk held at the 14th International Symposium on Mathematical
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\bibitem{ipm:Polyak8}
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\newblock Modified interior distance functions and center methods.
\newblock {Research Report} 17042~(75556), IBM Research Division T.\,J.\,Watson
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R.~Polyak.
\newblock Condition of the primal and dual linear programming problems.
\newblock {Talk held at the International Workshop on Computational
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  IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598, USA, 1992.

\bibitem{ipm:Polyak4}
R.~Polyak.
\newblock Modified barrier functions in linear programming.
\newblock {Research Report} 17790~(78331), Mathematical Sciences Department,
  IBM~T.\,J.\,Watson Research Center, Yorktown Heights, NY~10598, USA, 1992.

\bibitem{ipm:Polyak3}
R.~Polyak.
\newblock Modified barrier functions (theory and methods).
\newblock {\em Mathematical Programming}, 54:177--222, 1992.

\bibitem{ipm:Polyak20}
R.~Polyak.
\newblock Modified interior distance functions.
\newblock In S.~Cox et~al., editor, {\em Optimzation Methods in Partial
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\bibitem{ipm:Polyak7}
R.~Polyak and R.~R. Schneur.
\newblock Interior--exterior augmented {Lagrangian} approach for {LP}.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Mathematical Sciences Department, IBM~T.\,J.\,Watson Research
  Center, Yorktown Heights, NY~10598, USA, May 1992.

\bibitem{ipm:Ponceleon1}
D.~B. Poncele{\'o}n.
\newblock {\em Barrier methods for large--scale quadratic programming}.
\newblock PhD thesis, Computer Science Department, Stanford University,
  Stanford, CA~94305, USA, 1990.

\bibitem{ipm:Ponceleon2}
D.~B. Poncele{\'o}n.
\newblock Barrier methods for large--scale quadratic programming.
\newblock {Technical Report} SOL~91--2, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA~94305,
  USA, June 1991.

\bibitem{ipm:Ponnambalam1}
K.~Ponnambalam.
\newblock Large scale nonlinear programming using interior point and successive
  linear programming methods.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA}, Faculty
  of Engineering, Department of Electrical Engineering, University of Waterloo,
  Waterloo, Ontario~N2L~3G1, Canada, July 1990.

\bibitem{ipm:Ponnambalam5}
K.~Ponnambalam.
\newblock An interior point algorithm for large scale nonlinear programming.
\newblock {Talk held at the Symposium APMOD\,'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Faculty of Engineering, Department of Electrical Engineering, University of
  Waterloo, Waterloo, Ontario~N2L~3G1, Canada, January 1991.

\bibitem{ipm:Ponnambalam10}
K.~Ponnambalam.
\newblock An interior point algorithm for large scale nonlinear programming.
\newblock {Technical Report}, Department of Systems Design Engineering,
  University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1992.

\bibitem{ipm:Ponnambalam11}
K.~Ponnambalam, V.~H. Quintana, and A.~Vannelli.
\newblock A fast algorithm for power system optimization problems using an
  interior point method.
\newblock {\em IEEE Transactions on Power Systems}, 7:892--899, 1992.

\bibitem{ipm:Ponnambalam6}
K.~Ponnambalam, S.~Seetharaman, and T.~Alguindigue.
\newblock Affine algorithms for {$L$}--minimization.
\newblock In {\em Proceedings of the Sixth Multidimensional Signal Processing
  Workshop held in Pacific Grove, CA, USA, September 1989}, page 115. IEEE, New
  York, NY, USA, 1989.

\bibitem{ipm:Ponnambalam2}
K.~Ponnambalam and A.~Vannelli.
\newblock New starting and stopping steps for the dual affine variant of
  {Karmarkar's} method.
\newblock {Technical Report}, Faculty of Engineering, Department of Electrical
  Engineering, University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1988.

\bibitem{ipm:Ponnambalam3}
K.~Ponnambalam and A.~Vannelli.
\newblock An inexpensive basis recovery procedure for {Karmarkar's} dual affine
  method.
\newblock {Technical Report}, Faculty of Engineering, Department of Electrical
  Engineering, University of Waterloo, Waterloo, Ontario~N2L~3G1, Canada, 1989.

\bibitem{ipm:Ponnambalam9}
K.~Ponnambalam and A.~Vannelli.
\newblock Forcing a vertex optimal solution in interior point methods using an
  auxiliary function.
\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
  Programming and Modeling (APMOD\,'93), Budapest, Hungary, January 1993,
  Volume of Extended Abstracts}, pages 463--470. Computer and Automation
  Institute, Hungarian Academy of Sciences, Budapest, Hungary, December 1992.

\bibitem{ipm:Ponnambalam8}
K.~Ponnambalam, A.~Vannelli, E.~A. McBean, and T.~E. Unny.
\newblock Solving large--scale electric energy production planning and
  pollution control problems with {Karmarkar} algorithms.
\newblock In G.~B. Dantzig and P.~Glynn, editors, {\em Proceedings of the
  Workshop on Resource Planning Under Uncertainty for Electric Power Systems
  held at Stanford University, January 1989}, pages 179--196. 1989.

\bibitem{ipm:Ponnambalam4}
K.~Ponnambalam, A.~Vannelli, and T.~E. Unny.
\newblock An application of {Karmarkar's} interior point linear programming
  algorithm for multi--reservoir operations optimization.
\newblock {\em Stochastic Hydrology and Hydraulics}, 3:17--29, 1992.

\bibitem{ipm:Ponnambalam7}
K.~Ponnambalam, A.~Vannelli, and S.~Woo.
\newblock An interior point method implementation for solving large planning
  problems in the oil refinery industry.
\newblock {\em Canadian Journal of Chemical Engineering}, 70:368--374, 1992.

\bibitem{ipm:Poore1}
A.~B. Poore and D.~Soria.
\newblock Continuation algorithms for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New Orleans,
  USA}, Department of Mathematics, Colorado State University, Fort Collins,
  CO~80253, USA, May 1987.

\bibitem{ipm:Portnoy1}
S.~Portnoy and R.~Koenker.
\newblock The {Gaussian Hare} and the {Laplacian Tortoise}\,: {Computability}
  of squared--error vs. absolute--error estimates.
\newblock {Technical Report}, Department of Statistics, University of Illinois
  at Urbana--Champaign, Urbana, Il~61820, USA, March 1997.

\bibitem{ipm:Portugal3}
L.~F. Portugal, F.~Bastos, J.~J. J{\'u}dice, J.~Paix{\~a}o, and T.~Terlaky.
\newblock An investigation of interior point algorithms for the linear
  transportation problem.
\newblock {\em SIAM Journal on Scientific Computing}, 17:1202--1223, 1996.

\bibitem{ipm:Portugal5}
L.~F. Portugal, L.~Fernandes, and J.~J. J{\'u}dice.
\newblock A truncated {Newton} interior--point algorithm for the solution of a
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\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
  Variational Problems\,: State--of--the--Art (Baltimore 1995)}, pages
  315--344. SIAM Publications, Philadelphia, PA, USA, 1997.

\bibitem{ipm:Portugal4}
L.~F. Portugal and J.~J. J{\'u}dice.
\newblock A hybrid algorithm for the solution of a single commodity spatial
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\newblock {Technical Report}, Department of Mathematics, University of Coimbra,
  Coimbra, Portugal, 1994.

\bibitem{ipm:Portugal1}
L.~F. Portugal, J.~J. J{\'u}dice, and L.~Vicente.
\newblock A comparison of block pivoting and interior--point algorithms for
  linear least squares problems with nonnegative variables.
\newblock {\em Mathematics of Computation}, 63:625--643, 1994.

\bibitem{ipm:Portugal2}
L.~F. Portugal, M.~G.~C. Resende, G.~Veiga, and J.~J. J{\'u}dice.
\newblock A truncated primal--infeasible dual--feasible network interior point
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\newblock {Technical Report}, Mathematical Sciences Research Center, AT~\&~T
  Bell Laboratories, Murray Hill, NJ~07974--0636, USA, 1994.
\newblock Revised August 1996.

\bibitem{ipm:Potra2}
F.~A. Potra.
\newblock Implementation of interior point methods on parallel and vector
  machines.
\newblock In P.~Gritzmann, R.~Hettich, R.~Horst, and E.~Sachs, editors, {\em
  Operations Research '91 (Extended Abstracts of the 16th Symposium on
  Operations Research held at the University of Trier, Germany, September
  1991)}, pages 179--181. Springer Verlag, Berlin, Germany, 1992.

\bibitem{ipm:Potra8}
F.~A. Potra.
\newblock On a predictor--corrector method for solving linear programs from
  infeasible starting points.
\newblock {Reports on Computational Mathematics}~34, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, October 1992.
\newblock See also Potra \cite{ipm:Potra11}, which is a combined version of
  Potra \cite{ipm:Potra7} and this entry.

\bibitem{ipm:Potra4}
F.~A. Potra.
\newblock Polynomial complexity versus fast local convergence for interior
  point methods.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Department of Management Sciences, The University of Iowa, Iowa
  City, IA~52242, USA, May 1992.

\bibitem{ipm:Potra7}
F.~A. Potra.
\newblock A quadratically convergent infeasible interior--point algorithm for
  linear programming.
\newblock {Reports on Computational Mathematics}~28, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, July 1992.
\newblock See also Potra \cite{ipm:Potra11}, which is a combined version of
  this entry and Potra \cite{ipm:Potra8}.

\bibitem{ipm:Potra11}
F.~A. Potra.
\newblock A quadratically convergent predictor--corrector method for solving
  linear programs from infeasible starting points.
\newblock {\em Mathematical Programming}, 67:383--406, 1994.
\newblock This is a combined version of Potra \cite{ipm:Potra7,ipm:Potra8}.

\bibitem{ipm:Potra6}
F.~A. Potra.
\newblock An infeasible interior--point predictor--corrector algorithm for
  linear programming.
\newblock {\em SIAM Journal on Optimization}, 6:19--32, 1996.

\bibitem{ipm:Potra14}
F.~A. Potra.
\newblock An {$O(n\,L)$} infeasible--interior--point algorithm for {LCP} with
  quadratic convergence.
\newblock {\em Annals of Operations Research}, 62:81--102, 1996.

\bibitem{ipm:Potra12}
F.~A. Potra and J.~F. Bonnans.
\newblock Infeasible path following algorithms for linear complementarity
  problems.
\newblock {INRIA Research Report} RR--2445, Institute National de Recherche en
  Informatique et Automatique (INRIA), F--78153~Roquencourt, France, December
  1994.
\newblock To appear in {\em Mathematics of Operations Research}. See also
  Bonnans and Potra \cite{ipm:Bonnans6}.

\bibitem{ipm:Potra17}
F.~A. Potra and R.~Sheng.
\newblock Homogeneous interior--point algorithms for semidefinite programming.
\newblock {Reports on Computational Mathematics}~82, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, November 1995.

\bibitem{ipm:Potra15}
F.~A. Potra and R.~Sheng.
\newblock A path--following method for {LCP} with superlinearly convergent
  iteration sequence.
\newblock {Reports on Computational Mathematics}~69, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, April 1995.

\bibitem{ipm:Potra21}
F.~A. Potra and R.~Sheng.
\newblock Superlinear convergence of a predictor--corrector method for
  semidefinite programming without central path neighborhood.
\newblock {Reports on Computational Mathematics}~91, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, August 1996.

\bibitem{ipm:Potra18}
F.~A. Potra and R.~Sheng.
\newblock Superlinear convergence of interior--point algorithms for
  semidefinite programming.
\newblock {Reports on Computational Mathematics}~86, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, April 1996.

\bibitem{ipm:Potra13}
F.~A. Potra and R.~Sheng.
\newblock A large--step infeasible--interior--point method for the
  {$P_{*}$}--matrix {LCP}.
\newblock {\em SIAM Journal on Optimization}, 7:318--335, 1997.

\bibitem{ipm:Potra19}
F.~A. Potra and R.~Sheng.
\newblock Predictor--corrector algorithms for solving $p_{*}(\kappa)$--matrix
  {LCP} from arbitrary positive starting points.
\newblock {\em Mathematical Programming}, 76:223--244, 1997.

\bibitem{ipm:Potra23}
F.~A. Potra and R.~Sheng.
\newblock On homogeneous interior--point algorithms for semidefinite
  programming.
\newblock {\em Optimization Methods and Software}, 9:161--184, 1998.

\bibitem{ipm:Potra22}
F.~A. Potra and R.~Sheng.
\newblock Superlinearly convergent infeasible--interior--point algorithm for
  degenerate {LCP}.
\newblock {\em Journal of Optimization Theory and Applications}, 97:249--269,
  1998.

\bibitem{ipm:Potra16}
F.~A. Potra and R.~Sheng.
\newblock A superlinearly convergent primal--dual infeasible--interior--point
  algorithm for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:1007--1028, 1998.

\bibitem{ipm:Potra20}
F.~A. Potra, R.~Sheng, and N.~Brixius.
\newblock {SDPHA\,: A MATLAB} implementation of homogeneous interior--point
  algorithms for semidefinite programming.
\newblock {Reports on Computational Mathematics} 100, Department of
  Mathematics, The University of Iowa, Iowa City, IA~52242, USA, April 1997.

\bibitem{ipm:Potra9}
F.~A. Potra and Y.~Shi.
\newblock On an efficient interior point method for solving entropy
  optimization problems.
\newblock {Reports on Computational Mathematics}~23, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, December 1991.

\bibitem{ipm:Potra3}
F.~A. Potra, R.~A. Tapia, and Y.~Zhang.
\newblock An interior--point method for linear complementarity problems with
  polynomial complexity and superlinear convergence.
\newblock {Technical Report} TR~91--23, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Potra5}
F.~A. Potra and Y.~Ye.
\newblock An interior--point algorithm for solving entropy optimization
  problems with globally linear and locally quadratic convergence.
\newblock {Working Paper} 90--10, Department of Management Sciences, The
  University of Iowa, Iowa City, IA~52242, USA, 1990.
\newblock See also Potra and Ye\,\cite{ipm:Potra10}.

\bibitem{ipm:Potra1}
F.~A. Potra and Y.~Ye.
\newblock Interior point methods for nonlinear complementarity problems.
\newblock {Reports on Computational Mathematics}~15, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, July 1991.

\bibitem{ipm:Potra10}
F.~A. Potra and Y.~Ye.
\newblock A quadratically convergent polynomial algorithm for solving entropy
  optimization problems.
\newblock {\em SIAM Journal on Optimization}, 3:843--860, 1993.
\newblock See also Potra and Ye\,\cite{ipm:Potra5}.

\bibitem{ipm:Powell9}
M.~J. Powell.
\newblock Log barrier methods for semi--infinite programming calculations.
\newblock In {\em Hellenic Research in Mathematics and Informatics\,'92}, pages
  23--43. Hellenic Mathematical Society, Athens, Greece, 1992.
\newblock See also Powell \cite{ipm:Powell7}.

\bibitem{ipm:Powell2}
M.~J.~D. Powell.
\newblock Karmarkar's algorithm\,: {A} view from nonlinear programming.
\newblock {\em Bulletin of the Institute of Mathematics and Its Applications},
  26(8--9):165--181, 1990.

\bibitem{ipm:Powell1}
M.~J.~D. Powell.
\newblock Is {Karmarkar's} method suitable for semi--infinite programming\,?
\newblock {Talk held at the Symposium APMOD\,'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  Department of Applied Mathematics and Theoretical Physics, University of
  Cambridge, Silver Street, Cambridge~CB3~9EW, United Kingdom, January 1991.
\newblock There is no underlying report.

\bibitem{ipm:Powell3}
M.~J.~D. Powell.
\newblock The complexity of {Karmarkar's} algorithm for linear programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
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  142--163. Longman, Burnt Hill, Harlow, Essex, United Kingdom, 1992.

\bibitem{ipm:Powell5}
M.~J.~D. Powell.
\newblock Interior point methods for semi--infinite programming calculations.
\newblock In K.~H. Phua, C.~M. Wang, W.~Y. Yeong, T.~Y. Leong, H.~T. Loh, K.~C.
  Tan, and F.~S. Chou, editors, {\em Optimization\,: Techniques and
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  held in Singapore 1992)}, pages 3--5. World Science Publishing, River Edge,
  NJ, USA, 1992.

\bibitem{ipm:Powell6}
M.~J.~D. Powell.
\newblock Some convergence properties of the shifted log barrier method for
  linear programming.
\newblock {Technical Report} DAMTP~1992/NA7, Department of Applied Mathematics
  and Theoretical Physics, University of Cambridge, Silver Street,
  Cambridge~CB3~9EW, United Kingdom, November 1992.
\newblock Revised January 1994. See also Powell \cite{ipm:Powell8}.

\bibitem{ipm:Powell7}
M.~J.~D. Powell.
\newblock Log barrier methods for semi--infinite programming calculations.
\newblock In E.~A. Lipitakis, editor, {\em Advances on Computer Mathematics and
  Its Applications}, pages 1--21. World Scientific, Singapore, 1993.
\newblock See also Powell \cite{ipm:Powell9}.

\bibitem{ipm:Powell4}
M.~J.~D. Powell.
\newblock On the number of iterations of {Karmarkar's} algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 62:153--197, 1993.

\bibitem{ipm:Powell8}
M.~J.~D. Powell.
\newblock Some convergence properties of the modified log barrier method for
  linear programming.
\newblock {\em SIAM Journal on Optimization}, 5:695--739, 1995.
\newblock See also Powell \cite{ipm:Powell6}.

\bibitem{ipm:Puthenpura1}
S.~Puthenpura, R.~Saigal, and L.~P. Sinha.
\newblock Application of the {LQ} factorization in implementing the {Karmarkar}
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\newblock {Technical Memorandum} 51173--900205--01TM, AT \& T Bell
  Laboratories, 1990.

\bibitem{ipm:Puthenpura2}
S.~Puthenpura, L.~Sinha, S.-C. Fang, and R.~Saigal.
\newblock Solving stochastic programming problems via {Kalman} filter and
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\newblock {\em European Journal of Operational Research}, 83:503--513, 1995.

\bibitem{ipm:Puzanova1}
E.~A. Puzanova.
\newblock Allowance for error in computer computations in the {Karmarkar}
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\newblock {\em Optimizatsiya}, 46(63):51--67, 1989.
\newblock (In Russian).

\bibitem{ipm:Qi1}
L.~Qi and J.~Sun.
\newblock A nonsmooth version of {Newton's} method and an interior point
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\newblock {Technical Report} 90--01, Department of Industrial Engineering and
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R.-J. Qi and S.~A. Zenios.
\newblock On the scalability of data--parallel decomposition algorithms for
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\newblock {\em Journal of Parallel and Distributed Computing}, 22:565--570,
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\newblock Interior point methods and integer programming problems.
\newblock Master's thesis, Faculty of Technical Mathematics and Informatics, TU
  Delft, NL--2628~CD~Delft, The Netherlands, 1993.

\bibitem{ipm:Quintana1}
V.~H. Quintana, A.~Vannelli, and K.~Ponnambalam.
\newblock A fast dual affine implementation for power optimization.
\newblock {\em IEEE Transactions on Power Systems}, 7:892--899, 1992.

\bibitem{ipm:Quist1}
A.~J. Quist, {E. de} Klerk, C.~Roos, and T.~Terlaky.
\newblock Copositive relaxation for general quadratic programming.
\newblock {\em Optimization Methods and Software}, 9:185--208, 1998.

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\newblock Asymptotic behavior of the affine scaling variant of {Karmarkar's}
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\newblock In {\em Proceedings of the XX--th Conference 'Mathematical
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\newblock An empirical comparison of {KORBX} against {RELAXT}, a special code
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\newblock {Technical Report}, AT\&T Bell Laboratories, Holmdel, NJ~07733, USA,
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\newblock On the convex programming approach to linear programming.
\newblock {\em Operations Research Letters}, 10:309--312, 1991.

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\newblock Deriving an unconstrained convex program for linear programming.
\newblock {\em Journal of Optimization Theory and Applications},
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\newblock An affine--scaling, nonsmooth {Newton} hybrid method for constrained
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\bibitem{ipm:Ralph2}
D.~Ralph and S.~J. Wright.
\newblock Superlinear convergence of an interior--point method for monotone
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\newblock In M.~C. Ferris and J.-S. Pang, editors, {\em Complementarity and
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K.~G. Ramakrishnan, N.~K. Karmarkar, and A.~P. Kamath.
\newblock An approximate dual projective algorithm for solving assignment
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\newblock In D.~S. Johnson and C.~C. McGeogh, editors, {\em Network Flows and
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K.~G. Ramakrishnan, M.~G.~C. Resende, and P.~M. Pardalos.
\newblock A branch and bound algorithm for the quadratic assignment problem
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\newblock In C.~A. Floudas and P.~M. Pardalos, editors, {\em
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M.~V. Ramana and P.~M. Pardalos.
\newblock Semidefinite programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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\bibitem{ipm:Ramana2}
M.~V. Ramana, L.~Tun{\c c}el, and H.~Wolkowicz.
\newblock Strong duality for semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 7:641--662, 1997.

\bibitem{ipm:Ramaswamy1}
S.~Ramaswamy and J.~E. Mitchell.
\newblock On updating the analytic center after addition of multiple cuts.
\newblock {DSES Technical Report} 37--94--423, Department of Decision Sciences
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S.~Ramaswamy and J.~E. Mitchell.
\newblock A long step cutting plane algorithm that uses the volumetric barrier.
\newblock {DSES Technical Report}, Department of Decision Sciences and
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\bibitem{ipm:Rao1}
C.~V. Rao, S.~J. Wright, and J.~B. Rawling.
\newblock Application of interior--point methods to model predictive control.
\newblock {\em Journal of Optimization Theory and Applications}, 99:723--757,
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\newblock {Technical Report} 1.0, Mathematical Sciences Research Center,
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\newblock North Holland, Amsterdam, The Netherlands, 1991.

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C.~Roos and J.-Ph. Vial.
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\newblock {Technical Report} 94--77, Faculty of Technical Mathematics and
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\newblock PhD thesis, Department of Computer Science and Applied Mathematics,
  Aston University, Birmingham~B4~7ET, United Kingdom, 1989.

\bibitem{ipm:Salhi1}
A.~Salhi and G.~R. Lindfield.
\newblock Effects of ordering and updating techniques on the performance of the
  {Karmarkar} algorithm.
\newblock {\em R.A.I.R.O. Recherche Operationnelle/Operations Research},
  25(2):209--236, 1991.

\bibitem{ipm:Salhi3}
A.~Salhi and G.~R. Lindfield.
\newblock Standard form {Karmarkar's} algorithm for structured linear
  programming.
\newblock In E.~F. Deprettere and A.~J. van~der Veen, editors, {\em Algorithms
  and Parallel VLSI Architectures, Vol.\,B\,: Proceedings of the International
  Workshop on Algorithms and Parallel VLSI Architectures, Pont--a--Mousson,
  France, June 1990}, pages 501--510. Elsevier Science Publishers, B.\,V.,
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\bibitem{ipm:Salhi4}
A.~Salhi, G.~R. Lindfield, and L.~G. Proll.
\newblock The role of duality in the efficient use of a variant of
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\newblock In I.~Maros, editor, {\em Symposium on Applied Mathematical
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\bibitem{ipm:Saltzman1}
M.~J. Saltzman.
\newblock Parallel implementation of interior point {LP} algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Department of Mathematical Sciences, Clemson University, Clemson,
  SC~29634--1907, USA, May 1990.
\newblock See Saltzman \cite{ipm:Saltzman5}.

\bibitem{ipm:Saltzman3}
M.~J. Saltzman.
\newblock {WRIP\,: A workbench for research in interior point methods}.
\newblock {Panel Discussion held at the ORSA/TIMS Joint National Meeting in
  Philadelphia, PA, USA}, Department of Mathematical Sciences, Clemson
  University, Clemson, SC~29634--1907, USA, October 1990.

\bibitem{ipm:Saltzman5}
M.~J. Saltzman.
\newblock Implementation of an interior point {LP} algorithm on a
  shared--memory vector multiprocessor.
\newblock In O.~Balci, R.~Sharda, and S.~A. Zenios, editors, {\em Operations
  Research and Computer Science: New Developments in Their Interfaces}, pages
  87--101. Pergamon Press, Oxford, United Kingdom, 1992.

\bibitem{ipm:Saltzman4}
M.~J. Saltzman and R.~Bixby.
\newblock Recovering an optimal {LP} basis from an interior point solution.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Mathematical Sciences, Clemson University, Clemson,
  SC~29634--1907, USA, April 1992.
\newblock See Bixby and Saltzman \cite{ipm:Bixby2}.

\bibitem{ipm:Saltzman2}
M.~J. Saltzman, R.~Subramaniam, and R.~E. Marsten.
\newblock Implementing an interior point {LP} algorithm on a supercomputer.
\newblock In R.~Sharda, B.~L. Golden, E.~Wasil, O.~Balci, and W.~Stewart,
  editors, {\em Impacts of Recent Computer Advances on Operations Research},
  pages 158--168. North Holland, Amsterdam, The Netherlands, 1989.

\bibitem{ipm:Samuelsen3}
C.~M. Samuelsen.
\newblock {\em The {Dikin--Karmarkar} principle for steepest descent}.
\newblock PhD thesis, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, 1992.

\bibitem{ipm:Samuelsen1}
C.~M. Samuelsen and R.~A. Tapia.
\newblock The {Dikin--Karmarkar} principle for steepest descent.
\newblock {Talk held at the Second International Conference on Industrial and
  Applied Mathematics (ICIAM~'91), Washington, DC, USA}, Department of
  Mathematical Sciences, Rice University, Houston, TX~77251, USA, July 1991.
\newblock See Samuelsen \cite{ipm:Samuelsen3}.

\bibitem{ipm:Samuelsen2}
C.~M. Samuelsen and R.~A. Tapia.
\newblock The {Dikin--Karmarkar} principle for steepest descent\,: {Avoiding}
  short steps.
\newblock {Technical Report} TR~91--20, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Sargent1}
R.~W.~H. Sargent.
\newblock A homework exercise\,--\,{The big--M problem}.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
  Optimization\,: The State--of--the--Art (Il Ciocco, Barga, Italy, September
  1993)}, volume 434 of {\em NATO ASI Series C}, pages 475--479. Kluwer
  Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Sasakawa1}
T.~Sasakawa.
\newblock A study on interior--point algorithms for linear programming.
\newblock Master's thesis, Department of Information Physics and Mathematical
  Engineering, UNiversity of Tokyo, Tokyo, Japan, 1988.
\newblock (In Japanese).

\bibitem{ipm:Saunders1}
M.~A. Saunders.
\newblock {Major Cholesky} would feel proud.
\newblock {\em ORSA Journal on Computing}, 6:23--27, 1994.

\bibitem{ipm:Saunders2}
M.~A. Saunders.
\newblock Cholesky--based methods for sparse least squares\,: {The} benefits of
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\newblock In L.~Adams and J.~L. Nazareth, editors, {\em Linear and Nonlinear
  Conjugate Gradient--Related Methods (Proceedings of the AMS--IMS--SIAM Joint
  Summer Research Conference, Seattle, WA, USA, July 9--13, 1995)}, pages
  92--100. SIAM Publications, Philadelphia, PA, USA, 1996.

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U.~Sch{\"a}ttler.
\newblock {\em An interior--point method for semi--infinite programming
  problems}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  1992.
\newblock See also Sch{\"a}ttler \cite{ipm:Schaettler2}.

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U.~Sch{\"a}ttler.
\newblock An interior--point method for semi--infinite programming problems.
\newblock {\em Annals of Operations Research}, 62:277--301, 1996.
\newblock See also Sch{\"a}ttler \cite{ipm:Schaettler1}.

\bibitem{ipm:Schmieta1}
S.~Schmieta and F.~Alizadeh.
\newblock Associative algebras, symmetric cones and polynomial time interior
  point algorithms.
\newblock {RUTCOR Research Report} RRR\,17--98, RUTCOR -- Rutgers Center for
  Operations Research, Hill Center for Mathematical Sciences, New Brunswick,
  NJ~08903, USA, 1998.

\bibitem{ipm:Schneider1}
W.~Schneider.
\newblock An inner point preprocessing procedure.
\newblock {Talk held at the DGOR--Jahrestagung in Stuttgart--Hohernheim,
  Germany}, Institut f{\"u}r Informatik, Universit{\"a}t Linz, P.~O.~Box,
  A--4040~Linz, Austria, September 1991.

\bibitem{ipm:Schneider2}
W.~Schneider.
\newblock Eine innere--punkt--prozedur zur beschleunigung des
  simplexalgorithmus (an interior--point procedure for speeding up the simplex
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\newblock {\em Operations Research Proceedings 1991}, pages 381--388, 1992.

\bibitem{ipm:Schoenlein1}
A.~Sch{\"o}nlein.
\newblock {Der Algorithmus von Karmarkar---Idee, Realisation, Beispiel und
  numerische Erfahrungen (The Karmarkar algorithm---idea, realisation, example
  and numerical experiences)}.
\newblock {\em Angewandte Informatik}, 8:344--353, 1986.
\newblock (In German).

\bibitem{ipm:Schreck1}
H.~Schreck.
\newblock Experiences with an implementation of {Karmarkar's} {LP}--algorithm.
\newblock In M.~J. Beckmann, K.~W. Gaede, K.~Ritter, and H.~Schneeweiss,
  editors, {\em Proceedings of the X.~Symposium on Operations Research, Munich,
  Germany, August 1985}, volume~54 of {\em Methods of Operations Research},
  pages 535--542. Anton Hain Meisenheim Verlag, K{\"o}nigstein--Taunus,
  Germany, 1986.

\bibitem{ipm:Schrijver1}
A.~Schrijver.
\newblock The new linear programming method of {Karmarkar}.
\newblock {\em CWI Newsletter}, 8:2--14, 1985.

\bibitem{ipm:Schrijver2}
A.~Schrijver.
\newblock {\em Theory of Linear and Integer Programming}, chapter 15.1\,:
  {Karmarkar's} polynomial--time algorithm for linear programming, pages
  190--194.
\newblock John Wiley\,\&\,Sons, New York, 1986.

\bibitem{ipm:Schrijver3}
A.~Schrijver.
\newblock The algorithm of {N.\,K.\,Karmarkar} for linear programming.
\newblock {Talk held at the 14th Conference on the Mathematics of Operations
  Research in Dalfsen, The Netherlands}, Centre for Mathematics and Computer
  Science (CWI), Kruislaan 413, NL--1098~SJ~Amsterdam, The Netherlands, January
  1990.

\bibitem{ipm:Schultz1}
G.~L. Schultz and R.~R. Meyer.
\newblock A structured interior point method.
\newblock {Technical Report} 934, Department of Computer Science, University of
  Wisconsin, Madison, WI~53706, USA, 1990.

\bibitem{ipm:Schultz3}
G.~L. Schultz and R.~R. Meyer.
\newblock An interior point method for block angular optimization.
\newblock {\em SIAM Journal on Optimization}, 1(4):583--602, 1991.

\bibitem{ipm:Schultz2}
H.~Schultz and W.~Pulleyblank.
\newblock Trends in optimization.
\newblock {\em OR/MS Today}, 18(4):20--25, August 1991.

\bibitem{ipm:Schweitzer1}
E.~Schweitzer.
\newblock An interior random vector algorithm for multistage stochastic linear
  programs.
\newblock {\em SIAM Journal on Optimization}, 8:956--972, 1998.

\bibitem{ipm:Seifi1}
A.~Seifi and L.~Tun{\c c}el.
\newblock A constant--potential infeasible--start interior--point algorithm
  with computational experiments and applications.
\newblock {\em Computational Optimization and Applications}, 9:107--152, 1998.

\bibitem{ipm:Setiono4}
R.~Setiono.
\newblock Interior dual proximal--point algorithm using preconditioned
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\newblock {\em Optimization}, 24:63--73, 1992.

\bibitem{ipm:Setiono2}
R.~Setiono.
\newblock Interior proximal--point algorithm for linear programs.
\newblock {\em Journal of Optimization Theory and Applications},
  74(3):425--444, 1992.

\bibitem{ipm:Setiono3}
R.~Setiono.
\newblock Interior dual least 2--norm algorithm for linear programs.
\newblock {\em Optimization}, 31:875--899, 1993.

\bibitem{ipm:Setiono1}
R.~Setiono.
\newblock Interior dual proximal--point algorithm for linear programs.
\newblock {\em European Journal of Operational Research}, 77:96--110, 1994.

\bibitem{ipm:Shanno1}
D.~F. Shanno.
\newblock Computing {Karmarkar} projections quickly.
\newblock {\em Mathematical Programming}, 41:61--71, 1988.

\bibitem{ipm:Shanno14}
D.~F. Shanno.
\newblock Current state of primal--dual interior code.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
  Mathematical Programming, Asimolar Conference Center, Pacific Grove, CA,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, March 1990.

\bibitem{ipm:Shanno3}
D.~F. Shanno.
\newblock Interior--point methods for linear programming\,: {The}
  state--of--the--art.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University, Busch
  Campus, New Brunswick, NJ~08903, USA, July 1990.

\bibitem{ipm:Shanno2}
D.~F. Shanno.
\newblock Interior--point methods for linear programming\,: {The}
  state--of--the--computational--art.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, RUTCOR\,--\,Rutgers Center of Operations Research,
  Rutgers University, Busch Campus, New Brunswick, NJ~08903, USA, January 1990.

\bibitem{ipm:Shanno12}
D.~F. Shanno.
\newblock An overview of interior point methods with implementation details and
  computational experience.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
  Programming and Modelling, Brunel University, London, United Kingdom},
  RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University, Busch
  Campus, New Brunswick, NJ~08903, USA, January 1991.

\bibitem{ipm:Shanno17}
D.~F. Shanno.
\newblock Computational experience with logarithmic barrier methods for linear
  and nonlinear complementarity problems.
\newblock {Research Report} RRR~18--93, RUTCOR\,--\,Rutgers Center of
  Operations Research, Rutgers University, Busch Campus, New Brunswick,
  NJ~08903, USA, 1993.

\bibitem{ipm:Shanno18}
D.~F. Shanno.
\newblock Computational methods for linear programming.
\newblock In E.~Spedicato, editor, {\em Algorithms for Continuous
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  1993)}, volume 434 of {\em NATO Advanced Science Institute Series C\,:
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  Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Shanno4}
D.~F. Shanno and A.~Bagchi.
\newblock A unified view of interior point methods for linear programming.
\newblock {\em Annals of Operations Research}, 22:55--70, 1990.

\bibitem{ipm:Shanno20}
D.~F. Shanno, M.~G. Breitfeld, and E.~M. Simantiraki.
\newblock Implementing barrier methods for nonlinear programming.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Shanno13}
D.~F. Shanno and T.~J. Carpenter.
\newblock {\em Log}--barrier methods for quadratic and linearly constrained
  nonlinear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, November 1991.

\bibitem{ipm:Shanno15}
D.~F. Shanno and T.~J. Carpenter.
\newblock Computational experience with large scale quadratic programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, April 1992.

\bibitem{ipm:Shanno16}
D.~F. Shanno and T.~J. Carpenter.
\newblock Interior point methods for large scale quadratic programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers
  University, Busch Campus, New Brunswick, NJ~08903, USA, May 1992.

\bibitem{ipm:Shanno5}
D.~F. Shanno and R.~E. Marsten.
\newblock On implementing {Karmarkar's} method.
\newblock {Working Paper} 85--01, Graduate School of Administration, University
  of California, Davis, CA~95616, USA, 1985.

\bibitem{ipm:Shanno6}
D.~F. Shanno and R.~E. Marsten.
\newblock Implementation of the {Karmarkar} algorithm within {XMP} framework.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami Beach,
  FL, USA}, Graduate School of Administration, University of California, Davis,
  CA~95616, USA, October 1986.

\bibitem{ipm:Shanno7}
D.~F. Shanno and R.~E. Marsten.
\newblock A reduced--gradient variant of {Karmarkar's} algorithm and
  null--space projections.
\newblock {\em Journal of Optimization Theory and Applications}, 57:383--397,
  1988.

\bibitem{ipm:Shanno8}
D.~F. Shanno and R.~E. Marsten.
\newblock Interior point methods for linear programming\,: {Ready} for
  production use.
\newblock {Workshop held at the ORSA/TIMS Joint National Meeting in New York,
  NY, USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers
  University, Busch Campus, New Brunswick, NJ~08903, USA, October 1989.

\bibitem{ipm:Shanno9}
D.~F. Shanno and R.~E. Marsten.
\newblock Set partitioning via interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, October 1989.

\bibitem{ipm:Shanno11}
D.~F. Shanno, R.~E. Marsten, M.~J. Saltzman, and R.~Subramaniam.
\newblock Solving set partitioning problems with cutting planes and an interior
  point method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, October 1989.

\bibitem{ipm:Shanno10}
D.~F. Shanno, C.~L. Monma, and K.~McShane.
\newblock Computational experience with a primal--dual method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, RUTCOR\,--\,Rutgers Center of Operations Research, Rutgers University,
  Busch Campus, New Brunswick, NJ~08903, USA, April 1988.
\newblock See McShane et al.\ \cite{ipm:McShane1}.

\bibitem{ipm:Shanno19}
D.~F. Shanno and E.~M. Simantiraki.
\newblock An infeasible--interior--point method to solve the linear
  complementarity problem.
\newblock {Research Report} RRR~7--95, RUTCOR\,--\,Rutgers Center for
  Operations Research, Rutgers University, Busch Campus, New Brunswick,
  NJ~08903, USA, March 1995.

\bibitem{ipm:Shanno21}
D.~F. Shanno and E.~M. Simantiraki.
\newblock Interior point methods for linear and nonlinear programming.
\newblock In ?, editor, {\em The State--of--the--Art in Numerical Analysis},
  volume~63 of {\em Institute of Mathematics with Applications Conference
  Series (New Series)}, pages 339--362. Oxford University Press, New York, USA,
  1997.

\bibitem{ipm:Sharifi1}
F.~{Sharifi Mokhtarian} and J.-L. Goffin.
\newblock A nonlinear analytic center cutting plane method for a class of
  convex programming problems.
\newblock {\em SIAM Journal on Optimization}, 8:1108--1131, 1998.

\bibitem{ipm:Shaw6}
D.~X. Shaw.
\newblock Fractional linear functions and the analysis of variants of
  {Karmarkar's} method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, October 1989.

\bibitem{ipm:Shaw10}
D.~X. Shaw.
\newblock {\em Projective interior point methods for linear programming}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Research, Columbia University, New York, NY~10027, USA, 1991.

\bibitem{ipm:Shaw1}
D.~X. Shaw.
\newblock Several computational considerations for projective behavior point
  methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Rider College, Lawrenceville, NJ~08648, USA, April 1992.

\bibitem{ipm:Shaw3}
D.~X. Shaw.
\newblock General structures of a class of potential reduction algorithms.
\newblock {Technical Report}, School of Industrial Engineering, Purdue
  University, West Lafayette, IN\,47907, USA, August 1993.

\bibitem{ipm:Shaw5}
D.~X. Shaw.
\newblock On the complexity of a class of projective interior point methods for
  linear programming.
\newblock {Technical Report}, School of Industrial Engineering, Purdue
  University, West Lafayette, IN\,47907, USA, 1993.
\newblock See also Goldfarb and Shaw \cite{ipm:Goldfarb14}.

\bibitem{ipm:Shaw4}
D.~X. Shaw.
\newblock A self--concordant symmetric path--following algorithm for linear
  programming.
\newblock {Technical Report}, School of Industrial Engineering, Purdue
  University, West Lafayette, IN\,47907, USA, August 1993.

\bibitem{ipm:Shaw2}
D.~X. Shaw.
\newblock General structures of primal scaling interior point methods.
\newblock In A.~Bachem, U.~Derigs, M.~J{\"u}nger, and R.~Schrader, editors,
  {\em Operations Research\,'93}, pages 470--473. Physica Verlag (A
  Springer--Verlag Company), Heidelberg, Germany, 1994.
\newblock See also Shaw\,\cite{ipm:Shaw3}.

\bibitem{ipm:Shaw7}
D.~X. Shaw and D.~Goldfarb.
\newblock A primal projective interior point method for linear programming.
\newblock {Talk held at the CORS/ORSA/TIMS Joint National Meeting in Vancouver,
  British Columbia, Canada}, Department of Industrial Engineering and
  Operations Research, Columbia University, New York, NY~10027, USA, May 1989.

\bibitem{ipm:Shaw8}
D.~X. Shaw and D.~Goldfarb.
\newblock A path--following projective interior point method for linear
  programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, Department of Industrial Engineering and Operations Research,
  Columbia University, New York, NY~10027, USA, October 1990.

\bibitem{ipm:Shaw9}
D.~X. Shaw and D.~Goldfarb.
\newblock On the complexity of a class of projective interior point methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
  USA}, Department of Industrial Engineering and Operations Research, Columbia
  University, New York, NY~10027, USA, November 1991.
\newblock See Goldfarb and Shaw \cite{ipm:Goldfarb14}.

\bibitem{ipm:Sheng3}
R.~Sheng and F.~A. Potra.
\newblock Nonsymmetric search directions for semidefinite programming.
\newblock {Preprint} ANL/MCS--P692--0997, Mathematics And Computer Science
  Division, Argonne National Laboratory, Argonne, IL~60439, USA, September
  1997.

\bibitem{ipm:Sheng1}
R.~Sheng and F.~A. Potra.
\newblock A quadratically convergent infeasible--interior--point algorithm for
  {LCP} with polynomial complexity.
\newblock {\em SIAM Journal on Optimization}, 7:304--317, 1997.

\bibitem{ipm:Sheng2}
R.~Sheng, F.~A. Potra, and J.~Ji.
\newblock On a general class of interior--point algorithms for semidefinite
  programming with polynomial complexity and superlinear convergence.
\newblock {Reports on Computational Mathematics}~89, Department of Mathematics,
  The University of Iowa, Iowa City, IA~52242, USA, 1996.

\bibitem{ipm:Sherali1}
H.~D. Sherali.
\newblock Algorithmic insights and a convergence analysis for a
  {Karmarkar--type} of algorithm for linear programming problems.
\newblock {\em Naval Research Logistics Quarterly}, 34:399--416, 1987.

\bibitem{ipm:Sherali2}
H.~D. Sherali, B.~O. Skarpness, and B.~Kim.
\newblock An assumption--free convergence analysis of the scaling algorithm for
  linear programs, with application to the ${L_1}$ estimation problem.
\newblock {\em Naval Research Logistics Quarterly}, 35:473--492, 1988.

\bibitem{ipm:Sherkat1}
V.~R. Sherkat and Y.~Ikura.
\newblock Experience with interior point optimization software for a fuel
  planning application.
\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:833--840, 1994.
\newblock See also\,: {\em Proceedings of the Power Industry Computer
  Application Conference 1993, 89--}.

\bibitem{ipm:Sheu1}
R.-L. Sheu and S.-C. Fang.
\newblock On the relationship of interior point methods.
\newblock {Technical Report}, Operations Research Program, North Carolina State
  University, Raleigh, NC~27695, USA, November 1991.
\newblock To appear in {\em International Journal of Mathematics and
  Mathematical Sciences}.

\bibitem{ipm:Sheu2}
R.-L. Sheu and S.-C. Fang.
\newblock Insights into interior point methods.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 36(3), 1992.

\bibitem{ipm:Sheu3}
R.-L. Sheu and S.-C. Fang.
\newblock On the generalized path--following methods for linear programming.
\newblock {\em Optimization}, 30:235--249, 1994.

\bibitem{ipm:Sheu4}
R.-L. Sheu and S.-Y. Wu.
\newblock A method of weighted centers for quadratic semi--infinite programming
  with warm start.
\newblock {Technical Report}, Department of Mathematics, National Cheng--Kung
  University, Tainan, Taiwan, 1994.

\bibitem{ipm:Sheu5}
R.-L. Sheu, S.-Y. Wu, and S.-C. Fang.
\newblock A primal--dual infeasible--interior--point algorithm for linear
  semi--infinite programming.
\newblock {\em Computers and Mathematics with Applications}, 29(8):7--18, 1995.

\bibitem{ipm:Shi4}
B.~Shi and X.~Zhou.
\newblock Projected gradient type method of centers for constrained
  optimization.
\newblock {\em Journal of Mathematical Research and Exposition}, 17:375--381,
  1997.

\bibitem{ipm:Shi2}
C.-J. Shi, A.~Vannelli, and J.~Vlach.
\newblock An improvement on {Karmarkar's} algorithm for integer programming.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Bulletin}, 21:23--28, 1992.

\bibitem{ipm:Shi1}
M.~G. Shi.
\newblock Some convergence problems of interior point algorithms for linear
  programming.
\newblock {\em Journal of the Tsinghua University}, 28(3):91--101, 1988.
\newblock (In Chinese).

\bibitem{ipm:Shi3}
Y.~Shi.
\newblock Solving linear systems involved in constrained optimization.
\newblock {\em Linear Algebra and Its Applications}, 229:175--189, 1995.

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\bibitem{ipm:Sturm8}
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\newblock An interior point method, based on rank--1 updates, for linear
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\newblock {\em Mathematical Programming}, 81:77--87, 1998.

\bibitem{ipm:Saunders3}
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\newblock Solving regularized linear programs using barrier methods and {KKT}
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\newblock {Technical Report} SOL\,96--04, Systems Optimization Laboratory,
  Department of Operations Research, Stanford University, Stanford, CA\,94305,
  USA, December 1996.

\bibitem{ipm:Sun1}
J.~Sun.
\newblock An affine--scaling method for linearly constrained convex programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Industrial Engineering and Management Science,
  Northwestern University, Evanston, IL~60208, USA, May 1991.

\bibitem{ipm:Sun3}
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\newblock A convergence proof for an affine--scaling algorithm for convex
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\newblock {\em Mathematical Programming}, 60:69--79, 1993.

\bibitem{ipm:Sun4}
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\newblock A convergence analysis for a convex version of {Dikin's} algorithm.
\newblock {\em Annals of Operations Research}, 62:357--374, 1996.

\bibitem{ipm:Sun2}
J.~Sun and L.~Qi.
\newblock An interior point algorithm of {$O(\sqrt{n} |\ln\varepsilon |)$}
  iterations for {$C^{1}$}--convex programming.
\newblock {\em Mathematical Programming}, 57:239--257, 1992.

\bibitem{ipm:Sun11}
J.~Sun, K.-E. Wee, and J.~Zhu.
\newblock An interior point method for solving a class of linear--quadratic
  stochastic programming problems.
\newblock In D.-Z. Du, L.~Qi, and R.~S. Womersley, editors, {\em Recent
  Advances in Nonsmooth Optimization}, pages 392--404. World Scientific
  Publishing Co., River Edge, NJ~07661, USA, 1995.

\bibitem{ipm:Sun10}
J.~Sun and G.~Zhao.
\newblock A quadratically convergent long--step interior--point method for
  nonlinear monotone variational inequality problems.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, April 1996.

\bibitem{ipm:Sun8}
J.~Sun and G.~Zhao.
\newblock Global linear and local quadratic convergence of a long--step
  adaptive--mode interior point method for some monotone variational inequality
  problems.
\newblock {\em SIAM Journal on Optimization}, 8:123--139, 1998.

\bibitem{ipm:Sun9}
J.~Sun and J.~Zhu.
\newblock A predictor--corrector method for extended linear--quadratic
  programming.
\newblock {\em Computers and Operations Research}, 23:755--767, 1996.

\bibitem{ipm:Sun6}
J.~Sun, J.~Zhu, and W.~K. Eng.
\newblock Computational experiments on {ELQP} problems using interior point
  methods.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, 1995.

\bibitem{ipm:Sun7}
J.~Sun, J.~Zhu, and G.~Zhao.
\newblock A quadratically convergent polynomial long--step algorithm for a
  class of nonlinear monotone complementarity problems.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, January 1996.

\bibitem{ipm:Sun5}
J.~Sun, J.~Zhu, and G.~Zhao.
\newblock A predictor--corrector algorithm for a class of nonlinear saddle
  point problems.
\newblock {\em SIAM Journal on Control and Optimization}, 35:532--551, 1997.

\bibitem{ipm:Swart1}
E.~R. Swart.
\newblock How {I} implemented the {Karmarkar} algorithm in one evening.
\newblock {\em APL Quote Quad}, 15(3):13--16, 1985.

\bibitem{ipm:Swart2}
E.~R. Swart.
\newblock A modified version of the {Karmarkar} algorithm.
\newblock {Research Report in Mathematics}~98, Department of Mathematics and
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\bibitem{ipm:Szymanski1}
P.~T. Szymanski and M.~D. Lemmon.
\newblock Interior point methods in the design of hierarchical controllers.
\newblock {\em Proceedings of the 1994 IEEE International Symposium on
  Intelligent Control (Columbus, Ohio, USA, August 1994)}, pages 33--38, 1994.

\bibitem{ipm:Tachat1}
D.~Tachat.
\newblock {\em Methodes interieures en programmation lineaire\,: {Elaboration}
  et mise en oeuvre de procedures de projection exacte et approchee {(Interior
  point methods for linear programming\,: Computing exact and approximate
  projections)}}.
\newblock PhD thesis, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1991.
\newblock (In French).

\bibitem{ipm:Takehara1}
H.~Takehara.
\newblock An interior point algorithm for large scale portfolio optimization.
\newblock {\em Annals of Operations Research}, 45:373--386, 1993.

\bibitem{ipm:Tamiz1}
M.~Tamiz.
\newblock {\em Design, implementation and testing a general linear programming
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\newblock PhD thesis, Department of Mathematics and Statistics, Brunel
  University, Uxbridge, Middlesex~UB8\,3PH, United Kingdom, 1986.

\bibitem{ipm:Tamura1}
A.~Tamura, H.~Takehara, K.~Fukuda, S.~Fujishige, and M.~Kojima.
\newblock A dual interior primal simplex method for linear programming.
\newblock {\em Journal of the Operations Research Society of Japan},
  31:413--429, 1988.

\bibitem{ipm:Tamura2}
T.~E. Tamura.
\newblock Characteristics of {Karmarkar} method compared with simplex method.
\newblock {\em Bulletin of Nagoya Institute of Technology (Nagoya, Japan)},
  38:251--256, 1986.
\newblock (In Japanese).

\bibitem{ipm:Tan1}
K.~C. Tan and R.~M. Freund.
\newblock Newton's method for general parametric center problem with
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\newblock {Technical Report} RR~457, Department of Mathematics, National
  University of Singapore, Singapore~0511, 1991.

\bibitem{ipm:Tanabe4}
K.~Tanabe.
\newblock Center flattening transformation and a centered {N}ewton method for
  linear programming.
\newblock {Technical Report}, The Institute of Statistical Mathematics,
  4--6--7~Minami Azabu, Minatoku, Tokyo~106, Japan, 1987.

\bibitem{ipm:Tanabe6}
K.~Tanabe.
\newblock Centered {Newton} method for liner programming and quadratic
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\newblock {\em Proceedings of the 8th Mathematical Programming Symposium in
  Japan}, pages 131--152, 1987.

\bibitem{ipm:Tanabe1}
K.~Tanabe.
\newblock Complementarity--enforced centered {N}ewton method for mathematical
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\newblock In K.~Tone, editor, {\em New Methods for Linear Programming}, pages
  118--144, The Institute of Statistical Mathematics, 4--6--7~Minami Azabu,
  Minatoku, Tokyo~106, Japan, 1987.

\bibitem{ipm:Tanabe2}
K.~Tanabe.
\newblock Centered {Newton} method for mathematical programming.
\newblock In M.~Iri and K.~Yajima, editors, {\em System Modelling and
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\bibitem{ipm:Tanabe3}
K.~Tanabe.
\newblock Centered {N}ewton method for linear programming exterior point
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\newblock {Talk held at the First International Symposium on Interior Point
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  Minatoku, Tokyo~106, Japan, January 1990.

\bibitem{ipm:Tanabe7}
K.~Tanabe.
\newblock Centered {Newton} method for linear programming\,: {Interior} and
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\newblock In K.~Tone, editor, {\em New Methods for Linear Programming~3}, pages
  98--100. Institute of Statistical Mathematics, Tokyo, Japan, 1990.
\newblock In Japanese.

\bibitem{ipm:Tanabe8}
K.~Tanabe.
\newblock Center {Newton} methods and differential geometry of optimization.
\newblock {Cooperative Research Report}~89, The Institute of Statistical
  Mathematics, 4--6--7~Minami Azabu, Minatoku, Tokyo~106, Japan, 1996.
\newblock Contains 38 references related to the subject.

\bibitem{ipm:Tanabe5}
K.~Tanabe and T.~Tsuchiya.
\newblock Global analysis of dynamical systems associated with {Karmarkar's}
  method for linear programming.
\newblock {\em Proceedings of the Annual Meeting of the Operations Research
  Society of Japan}, pages 132--133, 1987.

\bibitem{ipm:Tang1}
H.-W. Tang and G.-B. Li.
\newblock Karmarkar's algorithm and fractional linear programming.
\newblock {\em Journal of the Dalian Institute of Technology}, 25:79--83
  (suppl.), 1986.
\newblock (In Chinese).

\bibitem{ipm:Tapia1}
R.~A. Tapia.
\newblock Current research in numerical optimization.
\newblock {\em SIAM News}, 20:10--11, March 1987.

\bibitem{ipm:Tapia2}
R.~A. Tapia.
\newblock Accelerating interior--point methods.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, January 1990.

\bibitem{ipm:Tapia12}
R.~A. Tapia.
\newblock On the fundamental role of interior--point methodology in constrained
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\newblock {Technical Report} TR~97--06, Department of Computational and Applied
  Mathematics, Rice University, Houston, TX~77251, USA, 1997.

\bibitem{ipm:Tapia3}
R.~A. Tapia and Y.~Zhang.
\newblock An optimal basis identification technique for interior point linear
  programming methods.
\newblock {Technical Report} TR--89--01, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, April 1989.
\newblock Revised September 1990. Essentially contained in Tapia and Zhang
  \cite{ipm:Tapia7}.

\bibitem{ipm:Tapia4}
R.~A. Tapia and Y.~Zhang.
\newblock Accelerating the convergence of interior point methods.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
  Department of Mathematical Sciences, Rice University, Houston, TX~77251, USA,
  July 1990.

\bibitem{ipm:Tapia5}
R.~A. Tapia and Y.~Zhang.
\newblock A cubically convergent method for locating a nearby vertex in linear
  programming.
\newblock {\em Journal of Optimization Theory and Applications}, 67:217--225,
  1990.

\bibitem{ipm:Tapia7}
R.~A. Tapia and Y.~Zhang.
\newblock An optimal--basis identification technique for interior--point linear
  programming algorithms.
\newblock {\em Linear Algebra and Its Applications}, 152:343--363, 1991.

\bibitem{ipm:Tapia6}
R.~A. Tapia and Y.~Zhang.
\newblock A polynomial and superlinearly convergent primal--dual interior
  algorithm for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Mathematical Sciences, Rice University,
  Houston, TX~77251, USA, May 1991.

\bibitem{ipm:Tapia10}
R.~A. Tapia and Y.~Zhang.
\newblock Interpretation and optimality properties of the {Karmarkar}
  algorithm.
\newblock {Technical Report} (in preparation), Department of Mathematical
  Sciences, Rice University, Houston, TX~77251, USA, 1992.

\bibitem{ipm:Tapia11}
R.~A. Tapia and Y.~Zhang.
\newblock On the quadratic convergence of the singular {Newton's} method.
\newblock {\em SIAG/OPT Views--and--News, A forum for the SIAM Activity Group
  on Optimization}, 1:6--8, 1992.

\bibitem{ipm:Tapia8}
R.~A. Tapia, Y.~Zhang, M.~Saltzman, and A.~Weiser.
\newblock The {Mehrotra} predictor--corrector interior--point method as a
  perturbed composite {Newton} method.
\newblock {\em SIAM Journal on Optimization}, 6:47--56, 1996.

\bibitem{ipm:Tapia9}
R.~A. Tapia, Y.~Zhang, and Y.~Ye.
\newblock On the convergence of the iteration sequence in primal--dual interior
  point methods.
\newblock {\em Mathematical Programming}, 68:141--154, 1995.

\bibitem{ipm:Tarasov1}
S.~P. Tarasov, L.~G. Khachiyan, and I.~I. Erlikh.
\newblock The method of inscribed ellipsoids.
\newblock {\em Soviet Mathematics Doklady}, 37:226--230, 1988.

\bibitem{:Terlaky1}
T.~Terlaky.
\newblock A {Karmarkar} tipusu algoritmusokrol ({On Karmarkar} type
  algorithms).
\newblock {\em Alkalmazott Matematikai Lapok}, 15:133--162, 1990/91.
\newblock (In Hungarian, English summary).

\bibitem{ipm:Terlaky2}
T.~Terlaky.
\newblock {\em {Interior Point Algorithms of Mathematical Programming}},
  volume~5 of {\em Applied Optimization}.
\newblock Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Terlaky5}
T.~Terlaky.
\newblock An easy way to teach interior--point methods.
\newblock {Technical Report} 98--24, Faculty of Information Technology and
  Systems Subfaculty of Technical Mathematics and Informatics, Department of
  Statistics, Stochastic and Operations Research Delft University of
  Technology, P.O.\,Box\,5031, NL--2600~GA~Delft, The Netherlands, 1998.

\bibitem{ipm:Terlaky4}
T.~Terlaky and T.~Tsuchiya.
\newblock A note on {Mascarenhas'} counter example about global convergence of
  the affine scaling algorithm.
\newblock {Research Memorandum} 596, The Institute of Statistical Mathematics,
  4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, March 1996.

\bibitem{ipm:Terlaky3}
T.~Terlaky and J.-Ph. Vial.
\newblock Computing maximum likelihood estimators of convex density functions.
\newblock {Technical Report} 95--49, Faculty of Technical Mathematics and
  Informatics, TU Delft, NL--2600~GA~Delft, The Netherlands, 1995.

\bibitem{ipm:Thompson1}
R.~G. Thompson, P.~S. Dharmapala, J.~B. Diaz, M.~D. Gonzalez-Lima, and R.~M.
  Thrall.
\newblock {DEA} multiplier analytic center sensitivity with an illustrative
  application to independent oil companies.
\newblock {\em Annals of Operations Research}, 66:163--177, 1996.

\bibitem{ipm:Thys1}
R.~Thys and {C. van} Nuffelen.
\newblock An implementation of {Karmarkar's} interior point algorithm.
\newblock {Working Paper} 89--124, Department of Economics and Econometrics,
  University of Antwerpen, Antwerpen, Belgium, 1989.

\bibitem{ipm:Tits1}
A.~L. Tits and J.~L. Zhou.
\newblock A simple, quadratically convergent interior point algorithm for
  linear programming and convex quadratic programming.
\newblock In W.~W. Hager, D.~W. Hearn, and P.~M. Pardalos, editors, {\em
  Large--Scale Optimization\,: The State--of--the --Art}, pages 411--427.
  Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.

\bibitem{ipm:Todd1}
M.~J. Todd.
\newblock A review of {N. Karmarkar}.
\newblock {\em Computing Reviews}, 27:95--96, March 1986.

\bibitem{ipm:Todd6}
M.~J. Todd.
\newblock The effects of degeneracy and sparsity on {Karmarkar's} projective
  algorithm and its variants.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1988.
\newblock See Todd \cite{ipm:Todd9}.

\bibitem{ipm:Todd4}
M.~J. Todd.
\newblock Exploiting special structure in {Karmarkar's} algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 41:97--113, 1988.

\bibitem{ipm:Todd3}
M.~J. Todd.
\newblock Improved bounds and containing ellipsoids in {Karmarkar's} linear
  programming algorithm.
\newblock {\em Mathematics of Operations Research}, 13:650--659, 1988.

\bibitem{ipm:Todd2}
M.~J. Todd.
\newblock Polynomial algorithms for linear programming.
\newblock In H.~A. Eiselt, editor, {\em Advances in Optimization and Control,
  Proceedings of the Conference {''Optimization Days '86''} held at Montreal,
  Quebec, Canada, April/May 1986}, volume 302 of {\em Lecture Notes in
  Economics and Mathematical Systems}, pages 49--66. Springer Verlag, Berlin,
  Germany, 1988.

\bibitem{ipm:Todd11}
M.~J. Todd.
\newblock Anticipated behavior of {Karmarkar's} algorithm.
\newblock {Technical Report} 879, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, December 1989.

\bibitem{ipm:Todd7}
M.~J. Todd.
\newblock Recent developments and new directions in linear programming.
\newblock In M.~Iri and K.~Tanabe, editors, {\em Mathematical Programming\,:
  Recent Developments and Applications}, pages 109--157. Kluwer Academic Press,
  Dordrecht, The Netherlands, 1989.

\bibitem{ipm:Todd12}
M.~J. Todd.
\newblock Anticipated behavior of interior point methods for linear
  programming.
\newblock {Talk held at the Symposium on Mathematical Programming in
  Oberwolfach, Germany}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, January 1990.
\newblock See Todd \cite{ipm:Todd11}, Mizuno et al.\,%
  \cite{ipm:Mizuno4,ipm:Mizuno5}.

\bibitem{ipm:Todd5}
M.~J. Todd.
\newblock A {Dantzig--Wolfe--like variant of Karmarkar's} interior--point
  linear programming algorithm.
\newblock {\em Operations Research}, 38:1006--1018, 1990.

\bibitem{ipm:Todd9}
M.~J. Todd.
\newblock The effects of degeneracy, null and unbounded variables on variants
  of {Karmarkar's} linear programming algorithm.
\newblock In T.~F. Coleman and Y.~Li, editors, {\em Large--Scale Numerical
  Optimization, Papers from the Workshop held at Cornell University, Ithaca,
  NY, USA, October 1989}, volume~46 of {\em SIAM Proceedings in Applied
  Mathematics}, pages 81--91. Society of Industrial and Applied Mathematics
  (SIAM), Philadelphia, PA, USA, 1990.

\bibitem{ipm:Todd18}
M.~J. Todd.
\newblock Projected scaled steepest descent in {Kojima--Mizuno--Yoshise's}
  potential reduction algorithm for the linear complementarity problem.
\newblock {Technical Report} 950, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, December 1990.

\bibitem{ipm:Todd10}
M.~J. Todd.
\newblock The affine--scaling direction for linear programming is a limit of
  projective--scaling directions.
\newblock {\em Linear Algebra and Its Applications}, 152:93--105, 1991.

\bibitem{ipm:Todd26}
M.~J. Todd.
\newblock Another derivation of the {Karmarkar} direction for linear
  programming.
\newblock {Technical Report} 91--20, Computational Optimization Project, Center
  for Applied Mathematics, Cornell University, Ithaca, NY~14853--3801, USA,
  December 1991.

\bibitem{ipm:Todd22}
M.~J. Todd.
\newblock Playing with interior points.
\newblock {\em Mathematical Programming Society Committee on Algorithms (COAL)
  Newsletter}, 19:17--25, August 1991.

\bibitem{ipm:Todd24}
M.~J. Todd.
\newblock Probabilistic models in linear programming.
\newblock {\em Mathematics of Operations Research}, 16(4):671--693, 1991.

\bibitem{ipm:Todd13}
M.~J. Todd.
\newblock A low complexity interior point algorithm for linear programming.
\newblock {\em SIAM Journal on Optimization}, 2:198--209, 1992.

\bibitem{ipm:Todd8}
M.~J. Todd.
\newblock On {Anstreicher's} combined {phase\,I\,--\,phase\,II} projective
  algorithm for linear programming.
\newblock {\em Mathematical Programming}, 55:1--15, 1992.

\bibitem{ipm:Todd25}
M.~J. Todd.
\newblock Recent developments on interior point methods for linear programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, School of Operations Research and Industrial Engineering, Cornell
  University, Ithaca, NY~14853--3801, USA, May 1992.
\newblock There is no underlying report.

\bibitem{ipm:Todd19}
M.~J. Todd.
\newblock Combining {phase\,I and phase\,II} in a potential reduction algorithm
  for linear programming.
\newblock {\em Mathematical Programming}, 59:133--150, 1993.

\bibitem{ipm:Todd29}
M.~J. Todd.
\newblock A lower bound on the number of iterations of primal--dual
  interior--point methods for linear programming.
\newblock {Technical Report} 1050, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, March 1993.
\newblock Revised June 1993.

\bibitem{ipm:Todd28}
M.~J. Todd.
\newblock Analysis of interior--point methods for linear programming problems
  with variable upper bounds.
\newblock In S.~Gomez and J.~P. Hennart, editors, {\em Advances in Optimization
  and Numerical Analysis (Proceedings of the Sixth Workshop on Optimization and
  Numerical Analysis, Oaxaca, Mexico, 1992)}, volume 275 of {\em Mathematics
  and Its Applications}, pages 1--23. Kluwer Academic Publishers, Dordrecht,
  The Netherlands, 1994.

\bibitem{ipm:Todd27}
M.~J. Todd.
\newblock Interior--point algorithms for semi--infinite programming.
\newblock {\em Mathematical Programming}, 65:217--245, 1994.

\bibitem{ipm:Todd31}
M.~J. Todd.
\newblock On lower bound on the number of iteration of an interior--point
  algorithm for linear programming.
\newblock In D.~F. Griffiths and G.~A. Watson, editors, {\em Numerical Analysis
  1993}, volume 303 of {\em Pitman Research Notes in Mathematics}, pages
  237--259. Longman Scientific \& Technical, Harlow, United Kingdom, 1994.
\newblock See also Todd and Ye \cite{ipm:Todd33}.

\bibitem{ipm:Todd32}
M.~J. Todd.
\newblock Scaling, shifting and weighting in interior--point methods.
\newblock {\em Computational Optimization and Applications}, 3:305--315, 1994.

\bibitem{ipm:Todd30}
M.~J. Todd.
\newblock Theory and practice for interior--point methods.
\newblock {\em ORSA Journal on Computing}, 6:28--31, 1994.

\bibitem{ipm:Todd38}
M.~J. Todd.
\newblock On adjusting parameters in homotopy methods for linear programming.
\newblock In {\em Approximation Theory and Optimization}, pages 201--220.
  Cambridge University Press, Cambridge, UK, 1997.

\bibitem{ipm:Todd39}
M.~J. Todd.
\newblock On search directions in interior--point methods for semidefinite
  programming.
\newblock {Technical Report} 1205, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, October 1997.

\bibitem{ipm:Todd36}
M.~J. Todd.
\newblock Potential--reduction methods in mathematical programming.
\newblock {\em Mathematical Programming}, 76:3--45, 1997.

\bibitem{ipm:Todd40}
M.~J. Todd.
\newblock A short history of interior--point methods.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1998.

\bibitem{ipm:Todd14}
M.~J. Todd and B.~P. Burrell.
\newblock An extension of {Karmarkar's} algorithm for linear programming using
  dual variables.
\newblock {\em Algorithmica}, 1(4):409--424, 1986.

\bibitem{ipm:Todd15}
M.~J. Todd and C.~C. Gonzaga.
\newblock An ${O(\sqrt{n}L)}$--iteration large--step primal--dual affine
  algorithm for linear programming.
\newblock {Talk held at the First International Symposium on Interior Point
  Methods for Linear Programming\,: Theory and Practice, in Scheveningen, The
  Netherlands}, School of Operations Research and Industrial Engineering,
  Cornell University, Ithaca, NY~14853--3801, USA, January 1990.
\newblock See Gonzaga and Todd \cite{ipm:Gonzaga12}.

\bibitem{ipm:Todd34}
M.~J. Todd and S.~Herzel.
\newblock Interior point algorithms for a class of convex programming problems.
\newblock {Technical Report} 1097, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, June 1994.

\bibitem{ipm:Todd23}
M.~J. Todd, S.~Mizuno, and Y.~Ye.
\newblock Anticipated behavior of path--following algorithms for linear
  programming.
\newblock {Talk held at the Second Asilomar Workshop on Progress in
  Mathematical Programming, Asilomar, CA, USA}, School of Operations Research
  and Industrial Engineering, Cornell University, Ithaca, NY~14853--3801, USA,
  February 1990.
\newblock See Mizuno et al.\ \cite{ipm:Mizuno4}.

\bibitem{ipm:Todd37}
M.~J. Todd, K.~Toh, and R.~T{\"u}t{\"u}nc{\"u}.
\newblock On the {Nesterov--Todd} direction in semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:769--796, 1998.

\bibitem{ipm:Todd41}
M.~J. Todd, L.~Tun{\c c}el, and Y.~Ye.
\newblock Probabilistic analysis of two complexity measures for linear
  programming problems.
\newblock {Technical Report} TR~1219, School of Operations Research and
  Industrial Engineering, Cornell University, Ithaca, NY~14853--3801, USA,
  October 1998.
\newblock Also available as {\it{CORR 98--48, Department of Combinatorics and
  Optimization, University of Waterloo, Waterloo, Ontario, Canada, October
  1998}}.

\bibitem{ipm:Todd20}
M.~J. Todd and J.-Ph. Vial.
\newblock Todd's low--complexity algorithm is a predictor--corrector
  path--following method.
\newblock {\em Operations Research Letters}, 11:199--207, 1992.

\bibitem{ipm:Todd21}
M.~J. Todd and Y.~Wang.
\newblock A projective algorithm for convex quadratic programming.
\newblock {Technical Report}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1991.

\bibitem{ipm:Todd16}
M.~J. Todd and Y.~Wang.
\newblock On combined {phase\,I\,--\,phase\,II} projective methods for linear
  programming.
\newblock {\em Algorithmica}, 9(1):64--83, 1993.

\bibitem{ipm:Todd17}
M.~J. Todd and Y.~Ye.
\newblock A centered projective algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 15:508--529, 1990.

\bibitem{ipm:Todd33}
M.~J. Todd and Y.~Ye.
\newblock A lower bound on the number of iterations of long--step primal--dual
  linear programming algorithms.
\newblock {\em Annals of Operations Research}, 62:233--252, 1996.

\bibitem{ipm:Todd35}
M.~J. Todd and Y.~Ye.
\newblock Approximate {Farkas Lemmas} and stopping rules for iterative
  infeasible--point algorithms for linear programming.
\newblock {\em Mathematical Programming}, 81:1--21, 1998.

\bibitem{ipm:Toh2}
K.~C. Toh.
\newblock Search directions for primal--dual interior point methods in
  semidefinite programming.
\newblock {Technical Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, July 1997.

\bibitem{ipm:Toh1}
K.~C. Toh, M.~J. Todd, and R.~H. T{\"u}t{\"u}nc{\"u}.
\newblock {SDPT3 -- A MATLAB software package for semidefinite programming}.
\newblock {Manuscript}, School of Operations Research and Industrial
  Engineering, Cornell University, Ithaca, NY~14853--3801, USA, 1996.

\bibitem{ipm:Tolla2}
P.~Tolla.
\newblock Amelioration des performances de l'algorithme de {Karmarkar} dans le
  cas de programmes lineaires a variables bornees superieurement {(Improvment
  of the efficiency of {Karmarkar's algorithm} for linear programs with upper
  bounded variables)}.
\newblock Cahier~82, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, November 1987.
\newblock (In French).

\bibitem{ipm:Tolla1}
P.~Tolla.
\newblock Validation numerique de l'algorithme de {Karmarkar} {(Numerical
  validation of Karmarkar's algorithm)}.
\newblock Cahier~76, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, April 1987.
\newblock (In French).

\bibitem{ipm:Tolla6}
P.~Tolla.
\newblock New numerical results on {Karmarkar's} algorithm.
\newblock Cahier, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, 1988.

\bibitem{ipm:Tolla4}
P.~Tolla.
\newblock Elaboration de logiciels efficaces utilisant l'algorithme de
  {Karmarkar} {(Elaboration of a computationally efficient utilization of
  Karmarkar's algorithm)}.
\newblock In J.~P. Penot, editor, {\em New Methods in Optimization and Their
  Industrial Uses}, volume~87 of {\em International Series of Numerical
  Mathematics}, pages 173--190. Birkh{\"a}user Verlag, Basel, Switzerland,
  1989.
\newblock (In French).

\bibitem{ipm:Tolla3}
P.~Tolla.
\newblock Optimal termination criterion and optimal solution accuracy test in
  the {Karmarkar's} algorithm.
\newblock In C.~Brezinski, editor, {\em Numerical and Applied Mathematics,
  Part~II. Papers from the Twelfth IMACS World Congress on Scientific
  Computation in Paris, France, July 1988}, volume 1.2 of {\em IMACS Annals of
  Computational and Applied Mathematics}, pages 629--633. Baltzer Verlag,
  Basel, Switzerland, 1989.

\bibitem{ipm:Tolla5}
P.~Tolla.
\newblock Implementation and validation of interior point methods for linear
  programming.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, Laboratoire de Analyse et Modelisation de Systemes pour
  l'Aide a la Decision (LAMSADE), Universite de Paris Dauphine,
  F--75775~Paris~Cedex~16, France, July 1991.

\bibitem{ipm:Tomlin1}
J.~A. Tomlin.
\newblock Experimental results with an implementation of the projective method.
\newblock Early draft of Tomlin \cite{ipm:Tomlin2}, 1985.

\bibitem{ipm:Tomlin2}
J.~A. Tomlin.
\newblock An experimental approach to {Karmarkar's} projective method for
  linear programming.
\newblock {\em Mathematical Programming Study}, 31:175--191, 1987.

\bibitem{ipm:Tomlin3}
J.~A. Tomlin.
\newblock A note on comparing simplex and interior methods for linear
  programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 91--104. Springer Verlag, New
  York, 1989.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tomlin6}
J.~A. Tomlin and J.~J. Forrest.
\newblock Switching from interior to vertex solutions in {OSL (Optimization
  Subroutine Library)}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, IBM Almaden Research Center, San Jose, CA~95120, USA, April 1992.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tomlin4}
J.~A. Tomlin and J.~S. Welch.
\newblock Implementing an interior point method in a mathematical programming
  system\,: {Part\,I}.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Miami, FL,
  USA}, Ketron Management Science, Inc., Mountain View, CA~94040, USA, October
  1986.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

\bibitem{ipm:Tomlin5}
J.~A. Tomlin and J.~S. Welch.
\newblock Implementing an interior point method in a mathematical programming
  system.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New Orleans,
  USA}, Ketron Management Science, Inc., Mountain View, CA~94040, USA, May
  1987.
\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}, and Tomlin
  \cite{ipm:Tomlin3}.

\bibitem{ipm:Tomlin7}
J.~A. Tomlin and J.~S. Welsch.
\newblock {Mathematical Programming Systems}.
\newblock In E.~G. {Coffman, Jr.}, J.~K. Lenstra, and A.~H.~G. {Rinnooy Kan},
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\newblock See also Forrest and Tomlin \cite{ipm:Forrest2}.

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\newblock Projection methods in calculation.
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C.~B. Tompkins.
\newblock Some methods of computational attack on programming problems, other
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\newblock A hybrid method for linear programming.
\newblock {Technical Report} 85--B--1, Graduate School for Policy Science,
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\bibitem{ipm:Tone2}
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\newblock An implementation of a revised {Karmarkar} method.
\newblock {Technical Report}, Graduate School for Policy Science, Saitama
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\bibitem{ipm:Tone4}
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\newblock An {$O(\sqrt{n}L)$} iteration large--step logarithmic barrier
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\newblock {Research Report} 89--B--5, Graduate School for Policy Science,
  Saitama University, Urawa, Saitama~338, Japan, 1989.

\bibitem{ipm:Tone3}
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\newblock Linear programming and {Karmarkar} patents.
\newblock {\em Systems, Control and Information}, 34(5):209--215, April 1990.
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\bibitem{ipm:Tone6}
K.~Tone.
\newblock Remarks on potential versus barrier function methods for linear
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\newblock {\em Journal of the Operations Research Society of Japan},
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\bibitem{ipm:Tone5}
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\newblock An active--set strategy in interior point method for linear
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\newblock {\em Mathematical Programming}, 59:345--360, 1993.

\bibitem{ipm:Torabi1}
M.~Torabi.
\newblock Decomposed block {Cholesky} factorization in the {Karmarkar}
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
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\newblock Decomposed block {Cholesky} factorization in the {Karmarkar}
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\newblock {\em Computers and Mathematics with Applications}, 20(2):1--7, 1990.

\bibitem{ipm:Torres1}
G.~L. Torres and V.~H. Quintana.
\newblock Optimal power flow via interior point methods\,: {An} educational
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\newblock {\em Proceedings of the 1996 Canadian Conference on Electrical and
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\bibitem{ipm:Tovey1}
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\newblock Integrating {Karmarkar's} algorithm into the curriculum.
\newblock {Workshop held at the ORSA/TIMS Joint National Meeting in Miami
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C.~A. Tovey.
\newblock The challenge\,: {Teaching Karmarkar's} algorithm.
\newblock {\em OR/MS Today}, 15(2):18--19, April 1988.

\bibitem{ipm:Trafalis2}
T.~B. Trafalis.
\newblock {\em Efficient faces of a polytope\,: {Interior} methods in multiple
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\newblock PhD thesis, Department of Mathematics and Computer Science, School of
  Industrial Engineering, Purdue University, West Lafayette, IN~47907, USA,
  August 1989.

\bibitem{ipm:Trafalis3}
T.~B. Trafalis.
\newblock Interior point methods in backpropagation neural networks.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
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  OK~73019, USA, November 1991.

\bibitem{ipm:Trafalis4}
T.~B. Trafalis.
\newblock A method of centers that computes {Pareto} solutions of cooperative
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, School of Industrial Engineering, University of Oklahoma, Norman,
  OK~73019, USA, April 1992.

\bibitem{ipm:Trafalis5}
T.~B. Trafalis and N.~P. Cou{\"e}llan.
\newblock Neural network training via a primal--dual interior point method for
  linear programming.
\newblock In {\em Proceedings of the World Congress on Neural Networks, Vol. 2
  (San Diego, June 1994)}, pages 798--803. Lawrence Erlbaum Associates,
  Hillsdale, NJ, USA, 1994.

\bibitem{ipm:Trafalis6}
T.~B. Trafalis and N.~P. Cou{\"e}llan.
\newblock Neural network training via an affine scaling quadratic optimization
  algorithm.
\newblock {\em Neural Networks}, 9:475--481, 1996.

\bibitem{ipm:Trafalis10}
T.~B. Trafalis, N.~P. Couellan, and S.~C. Bertrand.
\newblock Training of supervised neural networks via a nonlinear primal--dual
  interior--point method.
\newblock {\em IEEE Proceedings of the International Conference on Neural
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\bibitem{ipm:Trafalis1}
T.~B. Trafalis and T.~L. Morin.
\newblock Interior point methods in multiobjective convex optimization.
\newblock {Talk held at the TIMS/SOBRAPO Joint International Meeting in Rio de
  Janeiro, Brazil}, School of Industrial Engineering, University of Oklahoma,
  Norman, OK~73019, USA, July 1991.

\bibitem{ipm:Trafalis7}
T.~B. Trafalis and R.~K. Parekh.
\newblock Primal--dual training of artificial neural networks with an
  $l_{\infty}$ error.
\newblock {\em Proceedings of the Conference on Artificial Neural Networks in
  Engineering (ANNIE\,'95)}, pages 233--238, 1995.

\bibitem{ipm:Trafalis9}
T.~B. Trafalis, T.~Terlaky, J.~P. Warners, and C.~Roos.
\newblock Unsupervised neural network training via a potential reduction
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\newblock {Technical Report} 96--172, Faculty of Technical Mathematics and
  Informatics, Delft University of Technology, NL--2600 Delft, The Netherlands,
  1996.

\bibitem{ipm:Trafalis8}
T.~B. Trafalis, T.~A. Tutunji, and N.~P. Cou{\"e}llan.
\newblock Interior point methods for supervised training of artificial neural
  networks with bounded weights.
\newblock In P.~M. Pardalos, D.~W. Hearn, and W.~W. Hager, editors, {\em
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H.-S.~J. Tsao and S.-C. Fang.
\newblock An unconstrained dual approach to solving {Karmarkar--type} linear
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\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
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P.~Tseng.
\newblock A simple complexity proof for a polynomial--time linear programming
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\newblock {\em Operations Research Letters}, 8:155--159, 1989.

\bibitem{ipm:Tseng5}
P.~Tseng.
\newblock Path following by alternating minimization.
\newblock {Technical Report}, Department of Mathematics, GN--50, University of
  Washington, Seattle, WA~98195, USA, April 1991.

\bibitem{ipm:Tseng6}
P.~Tseng.
\newblock Complexity analysis of a linear complementarity algorithm based on a
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\newblock {\em Mathematical Programming}, 53:297--306, 1992.

\bibitem{ipm:Tseng2}
P.~Tseng.
\newblock Global linear convergence of a path--following algorithm for some
  monotone variational inequality problems.
\newblock {\em Journal of Optimization Theory and Applications},
  75(2):265--279, 1992.

\bibitem{ipm:Tseng4}
P.~Tseng.
\newblock A path--following algorithm for linear programming using quadratic
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\newblock {\em SIAM Journal on Control and Optimization}, 31:1578--1598, 1993.

\bibitem{ipm:Tseng7}
P.~Tseng.
\newblock Partial affine scaling for linearly constrained minimization.
\newblock {\em Mathematics of Operations Research}, 20:678--694, 1995.

\bibitem{ipm:Tseng8}
P.~Tseng.
\newblock Simplified analysis of an $o(nl)$--iteration infeasible
  predictor--corrector path--following method for monotone linear
  complementarity problems.
\newblock In R.~P. Agarwal, editor, {\em Recent Trends in Optimization Theory
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\bibitem{ipm:Tseng9}
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\newblock Search directions and convergence analysis of some infeasible
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\newblock {Technical Report}, Department of Mathematics, GN--50, University of
  Washington, Seattle, WA~98195, USA, 1996.

\bibitem{ipm:Tseng10}
P.~Tseng.
\newblock Analysis of an infeasible interior path--following method for
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\newblock {Technical Report}, Department of Mathematics, GN--50, University of
  Washington, Seattle, WA~98195, USA, August 1997.
\newblock Revised September 1997.

\bibitem{ipm:Tseng3}
P.~Tseng and Z.~Q. Luo.
\newblock On the convergence of the affine--scaling algorithm.
\newblock {\em Mathematical Programming}, 52:301--319, 1992.

\bibitem{ipm:Tsuchiya5}
T.~Tsuchiya.
\newblock Dual standard form linear programming problems and {Karmarkar's}
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\newblock {\em Lecture Note of the Research Institute of Statistical
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\newblock (In Japanese).

\bibitem{ipm:Tsuchiya4}
T.~Tsuchiya.
\newblock On {Yamashita's method and Freund's method} for linear programming.
\newblock {\em Cooperative Research Report of the Institute of Statistical
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\newblock (In Japanese).

\bibitem{ipm:Tsuchiya3}
T.~Tsuchiya.
\newblock Degenerate linear programming problems and the affine scaling method.
\newblock {\em Systems, Control and Information}, 34(4):216--222, April 1990.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya1}
T.~Tsuchiya.
\newblock Global convergence of the affine scaling methods for degenerate
  linear programming problems.
\newblock {\em Mathematical Programming}, 52:377--404, 1991.

\bibitem{ipm:Tsuchiya7}
T.~Tsuchiya.
\newblock Local analysis of {Iri and Imai's} method for degenerate linear
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\newblock {Research Memorandum (in preparation)}, The Institute of Statistical
  Mathematics, 4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, 1991.
\newblock This report has been finished as Tsuchiya \cite{ipm:Tsuchiya8}.

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T.~Tsuchiya.
\newblock {\em A study on the global and local convergence properties of the
  interior point algorithms for linear programming}.
\newblock PhD thesis, Faculty of Engineering, The University of Tokyo, Tokyo,
  Japan, 1991.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya6}
T.~Tsuchiya.
\newblock Global convergence property of the affine scaling methods for primal
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\newblock {\em Mathematics of Operations Research}, 17(3):527--557, 1992.

\bibitem{ipm:Tsuchiya11}
T.~Tsuchiya.
\newblock Global convergence of the affine scaling algorithm for primal
  degenerate strictly convex quadratic programming problems.
\newblock {\em Annals of Operations Research}, 46/47:509--539, 1993.

\bibitem{ipm:Tsuchiya15}
T.~Tsuchiya.
\newblock A new family of polynomial--time interior point algorithms for linear
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\newblock {Research Memorandum (in preparation)}, The Institute of Statistical
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\bibitem{ipm:Tsuchiya13}
T.~Tsuchiya.
\newblock Theoretical analysis of an affine scaling algorithm\,: {The} interior
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\newblock {\em Proceedings of the Institute of Statistical Mathematics},
  42:277--296, 1994.
\newblock (In Japanese).

\bibitem{ipm:Tsuchiya8}
T.~Tsuchiya.
\newblock Quadratic convergence of {Iri--Imai's} method for degenerate linear
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\newblock {\em Journal of Optimization Theory and Applications}, 87:703--726,
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\bibitem{ipm:Tsuchiya14}
T.~Tsuchiya.
\newblock Affine scaling algorithm.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
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\bibitem{ipm:Tsuchiya16}
T.~Tsuchiya.
\newblock A polynomial primal--dual path--following algorithm for second--order
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\newblock {Research Memorandum} 649, The Institute of Statistical Mathematics,
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\bibitem{ipm:Tsuchiya17}
T.~Tsuchiya.
\newblock A convergence analysis of the scaling--invariant primal--dual
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\newblock {Research Memorandum} 664, The Institute of Statistical Mathematics,
  4--6--7~Minami--Azabu, Minato--ku, Tokyo~106, Japan, 1998.

\bibitem{ipm:Tsuchiya12}
T.~Tsuchiya and R.~D.~C. Monteiro.
\newblock Superlinear convergence of the affine scaling algorithm.
\newblock {\em Mathematical Programming}, 75:77--110, 1996.

\bibitem{ipm:Tsuchiya10}
T.~Tsuchiya and M.~Muramatsu.
\newblock Global convergence of the long--step affine scaling algorithm for
  degenerate linear programming problems.
\newblock {\em SIAM Journal on Optimization}, 5:525--551, 1995.

\bibitem{ipm:Tsuchiya2}
T.~Tsuchiya and K.~Tanabe.
\newblock Local convergence properties of new methods in linear programming.
\newblock {\em Journal of the Operations Research Society of Japan}, 33:22--45,
  1990.

\bibitem{ipm:Tuncel2}
L.~Tun{\c{c}}el.
\newblock A note on the primal--dual affine scaling algorithms.
\newblock {Technical Report} 92--8, Computational Optimization Project, Center
  for Applied Mathematics, Cornell University, Ithaca, NY~14853--3801, USA, May
  1992.
\newblock For generalizations and extensions see Tun{\c{c}}el
  \cite{ipm:Tuncel4}.

\bibitem{ipm:Tuncel5}
L.~Tun{\c{c}}el.
\newblock A pseudo--polynomial complexity analysis for interior--point
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\newblock {Research Report} CORR\,93--16, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, 1993.

\bibitem{ipm:Tuncel4}
L.~Tun{\c{c}}el.
\newblock Constant potential primal--dual algorithms\,: {A} framework.
\newblock {\em Mathematical Programming}, 66:145--159, 1994.

\bibitem{ipm:Tuncel1}
L.~Tun{\c{c}}el.
\newblock On the convergence of primal--dual interior point methods with wide
  neighborhoods.
\newblock {\em Computational Optimization and Applications}, 4:139--158, 1995.

\bibitem{ipm:Tuncel6}
L.~Tun{\c{c}}el.
\newblock On the interplay among entropy, variable metrics and potential
  functions in interior--point algorithms.
\newblock {Research Report} CORR\,95--20, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, September 1995.
\newblock Also available as\,: Technical Report 1135, School of Operations
  Research and Industrial Engineering, Cornell University, Ithaca, NY~14853,
  USA, September 1995. See also Tun{\c{c}}el and Todd \cite{ipm:Tuncel8}.

\bibitem{ipm:Tuncel7}
L.~Tun{\c{c}}el.
\newblock Primal--dual symmetry and scale invariance of interior--point
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\newblock {Research Report} CORR\,96--18, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario, Canada, November 1996.

\bibitem{ipm:Tuncel9}
L.~Tun{\c{c}}el.
\newblock On the condition numbers for polyhedra in {Karmarkar's} form.
\newblock {Research Report} CORR\,97--24, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario~N2L\,3G1, Canada, November 1997.

\bibitem{ipm:Tuncel12}
L.~Tun{\c{c}}el.
\newblock Approximating the complexity measure of vavasis--ye algorithm is
  {NP--hard}.
\newblock {Research Report} CORR~98--51, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario~N2L\,3G1, Canada, November 1998.

\bibitem{ipm:Tuncel11}
L.~Tun{\c{c}}el.
\newblock Convex optimization: {Barrier} functions and interior-point methods.
\newblock {Research Report} B--336, Department of Combinatorics and
  Optimization, Faculty of Mathematics, University of Waterloo, Waterloo,
  Ontario~N2L\,3G1, Canada, March 1998.

\bibitem{ipm:Tuncel10}
L.~Tun{\c{c}}el.
\newblock Primal-dual potential reduction algorithms for semidefinite
  programming.
\newblock {Research Report}, Department of Combinatorics and Optimization,
  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario~N2L\,3G1,
  Canada, March 1998.
\newblock To appear as {\em{Potential reduction and primal-dual methods}},
  Semidefinite Programming and Applications, R. Saigal, L. Vandenberghe and H.
  Wolkowicz (eds.), Kluwer Academic Publishers, Boston, MA, USA.

\bibitem{ipm:Tuncel3}
L.~Tun{\c{c}}el and M.~J. Todd.
\newblock Asymptotic behavior of interior--point methods\,: {A} view from
  semi--infinite programming.
\newblock {\em Mathematics of Operations Research}, 21:354--381, 1996.

\bibitem{ipm:Tuncel8}
L.~Tun{\c{c}}el and M.~J. Todd.
\newblock On the interplay among entropy, variable metrics and potential
  functions in interior--point algorithms.
\newblock {\em Computational Optimization and Its Applications}, 8:5--19, 1997.
\newblock See also Tun{\c{c}}el \cite{ipm:Tuncel6}.

\bibitem{ipm:Turner1}
K.~Turner.
\newblock A variable metric variant of the {Karmarkar} algorithm for linear
  programming.
\newblock {Technical Report} TR--87--13, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1987.

\bibitem{ipm:Turner2}
K.~Turner.
\newblock Computing projections for the {Karmarkar} algorithm.
\newblock {\em Linear Algebra and Its Applications}, 152:141--154, 1991.

\bibitem{ipm:Tutuncu1}
R.~T{\"u}t{\"u}nc{\"u}.
\newblock An infeasible--interior--point potential--reduction algorithm for
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\newblock {Technical Report} 1136, School of Operations Research and Industrial
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\newblock PhD thesis, School of Operations Research and Industrial Engineering,
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\newblock An interior point algorithm for convex nonlinear programming
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\newblock {\em Numerical Mathematics (A Journal of Chinese Universities,
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\newblock (In Chinese).

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\newblock In D.~Pressmar, K.~E. Jaeger, H.~Krallmann, H.~Schellhaas, and
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\newblock Master's thesis, Faculty of Technical Mathematics and Informatics,
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\bibitem{ipm:Wei10}
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\newblock Interior point method for hydro--thermal optimal power flow.
\newblock {\em Proceedings of the 1995 International Conference on Energy
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\bibitem{ipm:Wei15}
H.~Wei, H.~Sasaki, and J.~Kubokawa.
\newblock Decoupled solution of hydro--thermal optimal power flow problem by
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\newblock {\em IEEE Transactions on Power Systems}, 13:286--293, 1998.

\bibitem{ipm:Wei13}
H.~Wei, H.~Sasaki, J.~Kubokawa, and R.~Yokoyama.
\newblock Interior point nonlinear programming method for optimal power flow
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\newblock {\em Proceedings of the 20th International Conference on Power
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\bibitem{ipm:Wei14}
H.~Wei, H.~Sasaki, J.~Kubokawa, and R.~Yokoyama.
\newblock Interior--point method for power system nonlinear {$L_{1}$} norm
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\newblock {\em IEEE Transactions on Power Systems}, 13:617--623, 1998.

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\newblock {\em Proceedings of the 1995 IEEE Power Industry Computer Application
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\newblock See also Wei et al. \cite{ipm:Wei11}.

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\newblock See also Wei et al. \cite{ipm:Wei8}.

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\newblock {\em Journal of Computational Mathematics}, 5:264--271, 1987.

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\newblock An interior point method for linear programming.
\newblock {\em Journal of Computational Mathematics}, 5:342--351, 1987.

\bibitem{ipm:Wei3}
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\newblock Some recent developments in linear programming.
\newblock {\em Mathematics in Practice and Theory}, 3:82--89, 1988.
\newblock (In Chinese).

\bibitem{ipm:Wei7}
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\newblock An estimate of {Lagrange} multipliers for linear programming using
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\newblock {\em Chinese Sciences Bulletin}, 37:1334--1338, 1992.

\bibitem{ipm:Wei5}
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\newblock The decomposition principle and algorithms for linear programs under
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\newblock {\em Chinese Sciences Bulletin}, 38:1585--1590, 1993.

\bibitem{ipm:Wei6}
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\newblock The decomposition principle and algorithms for linear programs under
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\newblock {\em Chinese Sciences Bulletin}, 38:1591--1595, 1993.

\bibitem{ipm:Wei12}
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\newblock An optimal basis identification criterion for interior point linear
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\newblock {\em Mathematica Numerica Sinica}, 18:215--224, 1996.
\newblock (In Chinese).

\bibitem{ipm:Wei4}
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\newblock Implementation of a dual interior algorithm for linear programming.
\newblock {\em Journal on Numerical Methods and Computer Applications},
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\newblock (In Chinese).

\bibitem{ipm:Wei9}
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\newblock A decomposition algorithm for linear programming under the interior
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\newblock {\em Journal on Numerical Methods and Computer Applications},
  16:99--108, 1995.
\newblock (In Chinese).

\bibitem{ipm:Werner1}
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\newblock {\em Numerische Mathematik~2 (Numerical Mathematics~2)}, chapter
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\newblock Vieweg Verlag, Braunschweig, Germany, 1992.

\bibitem{ipm:Winston1}
W.~L. Whinston.
\newblock {\em Operations Research\,: Applications and Algorithms}, chapter
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\newblock PWS--Kent Publishing Company, Boston, USA, second edition, 1992.

\bibitem{ipm:Whisman1}
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\newblock Optimization modelling in the military airlift command.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
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\newblock Linear programming and {H}uard's method of centres.
\newblock {Working Paper}, Universities of Manchester and Virginia, Manchester,
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\bibitem{ipm:Wiegers1}
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\newblock Implementation of the primal--dual interior point method for linear
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\newblock Master's thesis, Faculty of Electrical Engineering, Delft University
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\bibitem{ipm:Wild1}
W.~G. Wild and O.~Port.
\newblock The startling discovery {Bell Labs} kept in the shadows.
\newblock {\em {Business Week}}, September 21st 1987.

\bibitem{ipm:Williams1}
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\newblock An implementation of the affine scaling algorithm for linear
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\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Anaheim, CA,
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  Northridge, Los Angeles, CA~90024, USA, November 1991.

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\newblock A barrier function approach to mixed integer programming.
\newblock {Talk held at the Symposium APMOD~'91---Applied Mathematical
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\bibitem{ipm:Witzgall1}
C.~Witzgall, P.~T. Boggs, and P.~D. Domich.
\newblock On the convergence behavior of trajectories for linear programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
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\bibitem{ipm:Witzgall2}
C.~Witzgall, P.~T. Boggs, and P.~D. Domich.
\newblock On center trajectories and their relatives in linear programming.
\newblock {NISTIR Technical Report (in preparation)}, United States Department
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\newblock First draft in April 1988.

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\newblock {Technical Report}, Department of Combinatorics and Optimization,
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\bibitem{ipm:Wolkowicz2}
H.~Wolkowicz and Q.~Zhao.
\newblock Semidefinite programming relaxations for the graph partitioning
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\newblock {Technical Report}, Department of Combinatorics and Optimization,
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\newblock A brief history of linear programming.
\newblock {\em SIAM News}, 18(3):4, November 1985.

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M.~H. Wright.
\newblock Issues of numerical analysis in barrier trajectory methods.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
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\newblock See Wright \cite{ipm:Wright7,ipm:Wright9}, and Murray and Wright
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\newblock Interior methods for nonlinearly constrained optimization.
\newblock {Talk held at the SIAM Annual Meeting in Chicago, IL, USA},
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\newblock See Wright \cite{ipm:Wright7,ipm:Wright9}, and Murray and Wright
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M.~H. Wright.
\newblock Strategies in path--following methods for nonlinear constraints.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
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\newblock See Wright \cite{ipm:Wright7,ipm:Wright9}, and Murray and Wright
  \cite{ipm:Murray3}.

\bibitem{ipm:Wright5}
M.~H. Wright.
\newblock Linear algebra issues in interior methods.
\newblock {Talk held at the Fourth SIAM Conference on Applied Linear Algebra in
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\newblock See Wright \cite[Section\ 7]{ipm:Wright9}.

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\newblock Determining subspace information from the {Hessian} of a barrier
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\newblock {Numerical Analysis Manuscript} 92--02, AT~\&~T~Bell Laboratories,
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\newblock Interior methods for constrained optimization.
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\newblock Interior point methods for large--scale nonlinear optimization
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\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
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\newblock Some linear algebra issues in large--scale optimization.
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M.~H. Wright.
\newblock Why a pure primal {Newton} barrier step may be infeasible.
\newblock {\em SIAM Journal on Optimization}, 5:1--12, 1995.

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M.~H. Wright.
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\newblock {Technical Report} 98--4--09, Computing Sciences Research Center,
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\newblock {\em SIAM Journal on Optimization}, 9:84--111, 1999.

\bibitem{ipm:SWright3}
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\newblock {\em Proceedings of the 30th IEEE Conference on Decision and Control
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S.~J. Wright.
\newblock Convergence of an interior--point algorithm for linear
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\newblock {Technical Report} MCS--P340--1192, Mathematical and Computer Science
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\bibitem{ipm:SWright1}
S.~J. Wright.
\newblock An interior point algorithm for linearly constrained optimization.
\newblock {\em SIAM Journal on Optimization}, 2:450--473, 1992.

\bibitem{ipm:SWright4}
S.~J. Wright.
\newblock Structured interior point methods for stagewise extended linear
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\newblock {Talk held at the American Control Conference}, Mathematical and
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  USA, June 1992.
\newblock {Technical Report} in preparation.

\bibitem{ipm:SWright2}
S.~J. Wright.
\newblock Interior point methods for optimal control of discrete--time systems.
\newblock {\em Journal of Optimization Theory and Applications}, 77:161--187,
  1993.

\bibitem{ipm:SWright8}
S.~J. Wright.
\newblock A path--following infeasible--interior--point algorithm for linear
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\newblock {\em Optimization Methods and Software}, 2:79--106, 1993.

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S.~J. Wright.
\newblock An infeasible--interior--point algorithm for linear complementarity
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\newblock {\em Mathematical Programming}, 67:29--51, 1994.

\bibitem{ipm:SWright12}
S.~J. Wright.
\newblock Stability of linear algebra computations in interior--point methods
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\newblock {Preprint} MCS--P446--0694, Mathematical and Computer Science
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\newblock Revised July 1995.

\bibitem{ipm:SWright11}
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\newblock Stability of linear equations solvers in interior--point methods.
\newblock {\em SIAM Journal on Matrix Analysis and Applications},
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\bibitem{ipm:SWright14}
S.~J. Wright.
\newblock Modified {Cholesky} factorizations in interior--point algorithms for
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\newblock {Technical Report} ANL/MCS--P600--0596, Mathematical and Computer
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\newblock Revised June 1998.

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S.~J. Wright.
\newblock A path--following interior--point method for linear and quadratic
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\newblock {\em Annals of Operations Research}, 62:103--130, 1996.

\bibitem{ipm:SWright13}
S.~J. Wright.
\newblock {\em Primal--Dual Interior--Point Methods}.
\newblock SIAM Publications, SIAM, Philadelphia, PA, USA, 1996.

\bibitem{ipm:SWright16}
S.~J. Wright.
\newblock On the convergence of the {Newton}/log--barrier method.
\newblock {Preprint} ANL/MCS--P681--0897, Mathematical and Computer Science
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\bibitem{ipm:SWright15}
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\newblock Stability of augmented system factorizations in interior--point
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\newblock {\em SIAM Journal on Matrix Analysis and Applications}, 18:191--222,
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\bibitem{ipm:SWright17}
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\newblock Effects of finite--precision arithmetic on interior--point methods
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\newblock {Preprint} ANL/MCS--P705--0198, Mathematical and Computer Science
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\bibitem{ipm:SWright18}
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\newblock The role of linear objective functions in barrier methods.
\newblock {\em Mathematical Programming}, 84:357--373, 1999.

\bibitem{ipm:SWright7}
S.~J. Wright and D.~Ralph.
\newblock A superlinear infeasible--interior--point algorithm for monotone
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\newblock {\em Mathematics of Operations Research}, 21:815--838, 1996.

\bibitem{ipm:SWright9}
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\newblock A superquadratic infeasible--interior--point method for linear
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\newblock {\em Mathematical Programming}, 73:269--289, 1996.

\bibitem{ipm:Wu4}
F.~Wu, S.~Q. Wu, and Y.~Ye.
\newblock Convergence of the {$O(\sqrt{n}\,L)$}--iteration homogeneous and
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\newblock {Working Paper}, Department of Management Science, University of
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\bibitem{ipm:Wu7}
F.~Wu, S.~Q. Wu, and Y.~Ye.
\newblock On quadratic convergence of the homogeneous and self--dual linear
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\newblock {Working Paper}, Department of Management Science, University of
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\bibitem{ipm:Wu8}
J.~H. Wu.
\newblock Interior point algorithm for some monotone variational inequality
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\newblock {Preprint}, Center for Research on Transportation, University of
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\bibitem{ipm:Wu9}
J.~H. Wu.
\newblock Modified primal path--following scheme for the monotone variational
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\newblock {\em Journal of Optimization Theory and Applications}, 95:189--208,
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\bibitem{ipm:Wu6}
S.-P. Wu, S.~Boyd, and L.~Vandenberghe.
\newblock {FIR} filter design via semidefinite programming and spectral
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\newblock {\em Proceedings of the 35th IEEE Conference on Decision and
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S.~Q. Wu and F.~Wu.
\newblock New algorithms for linear programming.
\newblock {\em Acta Mathematica Applicatae Sinica (English Series)},
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\bibitem{ipm:Wu2}
S.~Q. Wu and F.~Wu.
\newblock A direct ellipsoid method for linear programming.
\newblock {\em Bulletin of the Australian Matehmatical Society}, 47(1):73--78,
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\bibitem{ipm:Wu3}
S.~Q. Wu and F.~Wu.
\newblock Rank--one techniques in log--barrier function methods for linear
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\newblock {\em Journal of Optimization Theory and Applications}, 82:405--413,
  1994.

\bibitem{ipm:Wu5}
Y.-C. Wu, A.~S. Debs, and R.~E. Marsten.
\newblock A direct nonlinear predictor--corrector primal--dual interior point
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\newblock {\em IEEE Transactions on Power Systems (PWRS)}, 9:876--883, 1994.
\newblock See also\,: {\em Proceedings of the Power Industry Computer
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\bibitem{ipm:Xu5}
C.-X. Xu.
\newblock Interior point algorithms for linear complementarity patterns.
\newblock {\em Journal on Numerical Methods and Computer Applications},
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\newblock (In Chinese).

\bibitem{ipm:Xu9}
S.~R. Xu.
\newblock The global linear convergence of an infeasible non--interior
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\newblock {Technical Report}, Department of Mathematics, University of
  Washington, Seattle, WA~98195, USA, December 1996.

\bibitem{ipm:Xu10}
S.~R. Xu and J.~V. Burke.
\newblock A polynomial time interior--point path following algorithm for {LCP}
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\newblock {Technical Report}, Department of Mathematics, University of
  Washington, Seattle, WA~98195, USA, September 1996.

\bibitem{ipm:Xu3}
S.~R. Xu and D.~Gong.
\newblock An interior point method for solving linear programming with hybrid
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\newblock {\em Acta Scientarium Naturalium Universitatis Sunyatseni},
  31(4):19--25, 1992.
\newblock (In Chinese).

\bibitem{ipm:Xu1}
S.~R. Xu, H.~B. Yao, and Y.~Q. Chen.
\newblock An improved {Karmarkar} algorithm for linear programming and its
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\newblock {\em Mathematica Applicata}, 5(1):14--21, 1992.
\newblock (In Chinese, English summary).

\bibitem{ipm:Xu11}
X.~Xu.
\newblock An infeasible interior--point algorithm for solving primal and dual
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\newblock {Working Paper}, Department of Management Science, University of
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\bibitem{ipm:Xu6}
X.~J. Xu.
\newblock {\em Interior point method for linear programming\,: {Theory} and
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\newblock PhD thesis, Institute of System Science, Academica Sinica, Beijing,
  China, 1991.

\bibitem{ipm:Xu8}
X.~J. Xu.
\newblock On the implementation of a homogeneous and self--dual linear
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\newblock {Technical Report}, College of Business Administration, University of
  Iowa, Iowa City, IA~52242, USA, 1994.

\bibitem{ipm:Xu7}
X.~J. Xu.
\newblock An $o(\sqrt{n}l)$--iteration large--step infeasible path--following
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\newblock {Technical Report}, College of Business Administration, University of
  Iowa, Iowa City, IA~52242, USA, August 1994.

\bibitem{ipm:Xu2}
X.~J. Xu, P.-F. Hung, and Y.~Ye.
\newblock A simplified homogeneous and self--dual linear programming algorithm
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\newblock {\em Annals of Operations Research}, 62:151--171, 1996.

\bibitem{ipm:Xu4}
X.~J. Xu and Y.~Ye.
\newblock A generalized homogeneous and self--dual algorithm for linear
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\newblock {\em Operations Research Letters}, 17:181--190, 1995.

\bibitem{ipm:Xuan1}
Z.~C. Xuan, X.~S. Li, and Y.~K. Sui.
\newblock An interior point method for solving surrogate dual problems in
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\newblock {\em Journal of the Dalian University of Technology}, 37:520--522,
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\newblock (In Chinese, English summary).

\bibitem{ipm:Xue1}
G.~Xue and Y.~Ye.
\newblock An efficient algorithm for minimizing a sum of {Euclidean} norms with
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\newblock {University of Vermont Research Report} CSEE/95/06--01, Department of
  Computer Science and Electrical Engineering, The University of Vermont,
  Burlington, VT~05405--0156, USA, June 1995.

\bibitem{ipm:Xue2}
G.~Xue and Y.~Ye.
\newblock An efficient algorithm for minimizing a sum of {P--norms}.
\newblock {Working Paper}, Department of Computer Science and Electrical
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\bibitem{ipm:Yabe1}
H.~Yabe and H.~Yamashita.
\newblock The speed of local convergence of a primal--dual interior point
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\newblock {\em S{\= u}rikaisekikenky{\= u}sho K{\= o}ky{\= u}roku (Proceedings
  of the Conference of the State of the Art of Scientific Computing and its
  Prospects, Kyoto, 1993)}, 880:211--219, 1994.
\newblock (In Japanese).

\bibitem{ipm:Yabe2}
H.~Yabe and H.~Yamashita.
\newblock Q--superlinear convergence of primal--dual interior point
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\newblock {\em Journal of the Operations Research Society of Japan},
  40:415--436, 1997.

\bibitem{ipm:Yamakawa1}
E.~Yamakawa, Y.~Matrsubara, and M.~Fukushima.
\newblock A parallel primal--dual interior point method for multicommodity flow
  problems with quadratic costs.
\newblock {\em Journal of the Operations Research Society of Japan},
  39:566--591, 1996.
\newblock (In Japanese).

\bibitem{ipm:Yamashita1}
H.~Yamashita.
\newblock A polynomially and quadratically convergent method for linear
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\newblock {Working Paper}, Mathematical Systems Institute, Inc., Shinjuku,
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\bibitem{ipm:Yamashita2}
H.~Yamashita.
\newblock A class of primal dual method for constrained optimization.
\newblock {Working Paper}, Mathematical Systems Institute, Inc., Tokyo, Japan,
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\bibitem{ipm:Yamashita5}
H.~Yamashita.
\newblock A globally convergent primal--dual interior point method for
  constrained optimization.
\newblock {\em Optimization Methods and Software}, 10:443--469, 1998.

\bibitem{ipm:Yamashita3}
H.~Yamashita and T.~Tanabe.
\newblock A primal--dual interior point method for linear and nonlinear
  programming.
\newblock {Talk held at the Fourth SIAM Conference on Optimization in Chicago,
  IL, USA}, Mathematical Systems Institute, Inc., Tokyo, Japan, May 1992.

\bibitem{ipm:Yamashita4}
H.~Yamashita and H.~Yabe.
\newblock Superlinear and quadratic convergence of some primal--dual interior
  point methods for constrained optimization.
\newblock {\em Mathematical Programming}, 75:377--397, 1996.

\bibitem{ipm:Yan1}
X.~Yan and V.~H. Quintana.
\newblock An efficient technique for solving dense row problems in
  security--constrained economic dispatch.
\newblock {\em Proceedings of the Twenty--Sixth Annual North American Power
  Symposium (Manhattan, KS, USA, September 1994)}, 2:568--574, 1994.

\bibitem{ipm:Yan3}
X.~Yan and V.~H. Quintana.
\newblock An infeasible interior--point algorithm for optimal power--flow
  problems.
\newblock {\em Electrical Power Systems Research}, 39:39--46, 1996.

\bibitem{ipm:Yan2}
X.~Yan and V.~H. Quintana.
\newblock An efficient predictor--corrector interior point algorithm for
  security--constrained economic dispatch.
\newblock {\em IEEE Transactions on Power Systems}, 12:803--810, 1997.

\bibitem{ipm:Yang4}
D.~Yang and S.~A. Zenios.
\newblock A scalable parallel interior point algorithm for stochastic linear
  programming and robust optimization.
\newblock {\em Computational Optimization and Applications}, 7:143--158, 1997.

\bibitem{ipm:Yang3}
E.~K. Yang and C.-H. Chou.
\newblock A method for solving least--squares problems arising from angular
  linear programs.
\newblock {\em Tamkang Journal of Mathematics}, 25:1--13, 1994.

\bibitem{ipm:Yang1}
E.~K. Yang and W.~S. Hwang.
\newblock An interior point method for dynamic {Leontief} type linear programs.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Las Vegas, NV,
  USA}, Institute of Applied Mathematics, Tsing Hua University, Hsinchu, 30043,
  People Republic of China, May 1990.
\newblock See Yang and Hwang \cite{ipm:Yang2}.

\bibitem{ipm:Yang2}
E.~K. Yang and W.~S. Hwang.
\newblock A barrier method for dynamic {Leontief} type linear programs.
\newblock {\em European Journal of Operational Research}, 60:296--305, 1992.

\bibitem{ipm:Yang6}
H.-H. Yang.
\newblock {\em Investigation of path--following algorithms for signomial
  geometric programming problems}.
\newblock PhD thesis, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1994.

\bibitem{ipm:Yang5}
H.-H. Yang and D.~L. Bricker.
\newblock Investigation of path--following algorithms for signomial geometric
  problems.
\newblock {\em European Journal of Operational Research}, 103:230--241, 1997.

\bibitem{ipm:Ye4}
Y.~Ye.
\newblock Barrier projection and sliding current objective method for linear
  programming.
\newblock {Talk held at the 12th Mathematical Programming Symposium, Boston,
  MA, USA}, Department of Engineering Economic Systems, Stanford University,
  Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Ye3}
Y.~Ye.
\newblock Cutting--objective and scaling methods---a polynomial algorithm for
  linear programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1985.
\newblock Submitted to {\em Mathematical Programming}.

\bibitem{ipm:Ye2}
Y.~Ye.
\newblock Cutting current--objective method in projective algorithm for linear
  programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, February 1985.

\bibitem{ipm:Ye46}
Y.~Ye.
\newblock K--projection and cutting--objective method for linear programming.
\newblock {Talk held at the 12th Mathematical Programming Symposium, Boston,
  MA, USA}, Department of Engineering Economic Systems, Stanford University,
  Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Ye1}
Y.~Ye.
\newblock A large group of projections for linear programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1985.

\bibitem{ipm:Ye40}
Y.~Ye.
\newblock A ''build--down'' simplex--{Karmarkar} method for linear programming.
\newblock {Technical Report}, Department of Engineering Economic Systems,
  Stanford University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye6}
Y.~Ye.
\newblock Dual approach of {Karmarkar's} algorithm and the ellipsoid method.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye7}
Y.~Ye.
\newblock Further development on the interior algorithm for convex quadratic
  programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye5}
Y.~Ye.
\newblock {\em Interior algorithms for linear, quadratic, and linearly
  constrained convex programming}.
\newblock PhD thesis, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1987.

\bibitem{ipm:Ye8}
Y.~Ye.
\newblock Karmarkar's algorithm and the ellipsoid method.
\newblock {\em Operations Research Letters}, 6:177--182, 1987.

\bibitem{ipm:Ye32}
Y.~Ye.
\newblock Bimatrix equilibrium points and potential functions.
\newblock {Working Paper} 88--16, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1988.

\bibitem{ipm:Ye10}
Y.~Ye.
\newblock The ''build--down'' scheme for path--following algorithms.
\newblock {Technical Report}, Integrated Systems Inc., Santa Clara, CA, USA,
  1988.

\bibitem{ipm:Ye11}
Y.~Ye.
\newblock A class of potential functions for linear programming.
\newblock {Management Science Working Paper} 88--13, Department of Management
  Science, University of Iowa, Iowa City, IA~52242, USA, 1988.

\bibitem{ipm:Ye38}
Y.~Ye.
\newblock On the interior algorithms for nonconvex quadratic programming.
\newblock {Manuscript}, Integrated Systems, Inc., Santa Clara, CA, USA, 1988.

\bibitem{ipm:Ye33}
Y.~Ye.
\newblock A combinatorial property of analytic centers of polytopes.
\newblock {Manuscript}, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye13}
Y.~Ye.
\newblock Eliminating columns and rows in potential reduction and
  path--following algorithms for linear programming.
\newblock {Working Paper Series} 89--7, Department of Management Science,
  University of Iowa, Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye14}
Y.~Ye.
\newblock An extension of {Karmarkar's} algorithm and the trust region method
  for quadratic programming.
\newblock In N.~Megiddo, editor, {\em Progress in Mathematical Programming\,:
  Interior Point and Related Methods}, pages 49--64. Springer Verlag, New York,
  1989.

\bibitem{ipm:Ye31}
Y.~Ye.
\newblock Further developments in potential reduction algorithm.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye28}
Y.~Ye.
\newblock Line searches in potential reduction algorithm for linear
  programming.
\newblock Manuscript, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1989.

\bibitem{ipm:Ye12}
Y.~Ye.
\newblock Potential functions and polytopes.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in New York, NY,
  USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, October 1989.

\bibitem{ipm:Ye34}
Y.~Ye.
\newblock Anticipated behavior of affine scaling algorithms for linear
  programming.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ye16}
Y.~Ye.
\newblock A ''build--down'' scheme for linear programming.
\newblock {\em Mathematical Programming}, 46:61--72, 1990.

\bibitem{ipm:Ye17}
Y.~Ye.
\newblock A class of projective transformations for linear programming.
\newblock {\em SIAM Journal on Computing}, 19:457--466, 1990.

\bibitem{ipm:Ye19}
Y.~Ye.
\newblock Complexity analysis on {Karmarkar's} algorithm.
\newblock {Manuscript}, Department of Management Science, University of Iowa,
  Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ye26}
Y.~Ye.
\newblock Interior point algorithms for global optimization.
\newblock {\em Annals of Operations Research}, 25:59--74, 1990.

\bibitem{ipm:Ye39}
Y.~Ye.
\newblock An {$O(n^{3}L)$} potential reduction algorithm for linear
  programming.
\newblock In J.~C. Lagarias and M.~J. Todd, editors, {\em Mathematical
  Developments Arising from Linear Programming\,: Proceedings of a Joint Summer
  Research Conference held at Bowdoin College, Brunswick, Maine, USA, June/July
  1988}, volume 114 of {\em Contemporary Mathematics}, pages 77--88. American
  Mathematical Society, Providence, Rhode Island, USA, 1990.

\bibitem{ipm:Ye48}
Y.~Ye.
\newblock The potential algorithm for linear complementarity problems.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1990.

\bibitem{ipm:Ye18}
Y.~Ye.
\newblock Recovering optimal basic variables in {Karmarkar's} polynomial
  algorithm for linear programming.
\newblock {\em Mathematics of Operations Research}, 15:564--572, 1990.

\bibitem{ipm:Ye15}
Y.~Ye.
\newblock Comparative analysis of affine scaling algorithms based on
  simplifying assumptions.
\newblock {\em Mathematical Programming}, 52:405--414, 1991.

\bibitem{ipm:Ye50}
Y.~Ye.
\newblock Improving the asymptotic convergence of interior--point algorithms
  for linear programming.
\newblock {Working Paper} 91--15, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.

\bibitem{ipm:Ye27}
Y.~Ye.
\newblock Interior point algorithms for quadratic programming.
\newblock In S.~Kumar, editor, {\em Recent Developments in Mathematical
  Programming}, pages 237--261. Gordon~\& Beach Scientific Publishers,
  Philadelphia, PA, USA, 1991.

\bibitem{ipm:Ye53}
Y.~Ye.
\newblock A low complexity combined {phase\,I\,--\,phase\,II} potential
  reduction algorithm for linear programming.
\newblock {Working Paper} 91--1, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.

\bibitem{ipm:Ye52}
Y.~Ye.
\newblock On the $q$--order of convergence of interior--point algorithms for
  linear programming.
\newblock {Working Paper} 91--17, Department of Management Science, University
  of Iowa, Iowa City, IA~52242, USA, 1991.
\newblock Also published in {\em W. Fang (ed.), Proceedings of the 1992
  Symposium on Applied Mathematics, Institute of Applied Mathematics, Chinese
  Academy of Sciences, 1992, pp. 534--543}.

\bibitem{ipm:Ye9}
Y.~Ye.
\newblock An ${O(n^{3}L)}$ potential reduction algorithm for linear
  programming.
\newblock {\em Mathematical Programming}, 50:239--258, 1991.

\bibitem{ipm:Ye49}
Y.~Ye.
\newblock Extensions of the potential reduction algorithm for linear
  programming.
\newblock {\em Journal of Optimization Theory and Applications},
  72(3):487--498, 1992.

\bibitem{ipm:Ye25}
Y.~Ye.
\newblock A further result on the potential reduction algorithm for the
  {$P$}--matrix linear complementarity problem.
\newblock In P.~M. Pardalos, editor, {\em Advances in Optimization and Parallel
  Computing}, pages 310--316. North Holland, Amsterdam, The Netherlands, 1992.

\bibitem{ipm:Ye29}
Y.~Ye.
\newblock On an affine scaling algorithm for nonconvex quadratic programming.
\newblock {\em Mathematical Programming}, 52:285--300, 1992.

\bibitem{ipm:Ye35}
Y.~Ye.
\newblock On the finite convergence of interior--point algorithms for linear
  programming.
\newblock {\em Mathematical Programming}, 57:325--335, 1992.

\bibitem{ipm:Ye41}
Y.~Ye.
\newblock A potential reduction algorithm allowing column generation.
\newblock {\em SIAM Journal on Optimization}, 2:7--20, 1992.

\bibitem{ipm:Ye30}
Y.~Ye.
\newblock A fully polynomial--time approximation algorithm for computing a
  stationary point of the generalized linear complementarity problem.
\newblock {\em Mathematics of Operations Research}, 18:334--345, 1993.

\bibitem{ipm:Ye45}
Y.~Ye.
\newblock Toward probabilistic analysis of interior--point algorithms for
  linear programming.
\newblock {\em Mathematics of Operations Research}, 19:38--52, 1994.

\bibitem{ipm:Ye54}
Y.~Ye.
\newblock On the {von Neumann} economic growth problem.
\newblock {\em Mathematics of Operations Research}, 20:617--633, 1995.

\bibitem{ipm:Ye59}
Y.~Ye.
\newblock Convergence behavior of the central path homogeneous and self--dual
  cones.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1996.

\bibitem{ipm:Ye61}
Y.~Ye.
\newblock How partial knowledge helps to solve linear programs.
\newblock {\em Journal of Complexity}, 12:480--491, 1996.

\bibitem{ipm:Ye64}
Y.~Ye.
\newblock Approximating quadratic optimization with linear and boolean
  constraints.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, August 1997.

\bibitem{ipm:Ye63}
Y.~Ye.
\newblock Approximating quadratic programming with bound constraints.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, March 1997.

\bibitem{ipm:Ye56}
Y.~Ye.
\newblock Complexity analysis of the analytic center cutting plane method that
  uses multiple cuts.
\newblock {\em Mathematical Programming}, 78:85--104, 1997.

\bibitem{ipm:Ye57}
Y.~Ye.
\newblock {\em {Interior--Point Algorithms\,: Theory and Practice}}.
\newblock John Wiley\,\&\, Sons, New York, USA, 1997.

\bibitem{ipm:Ye60}
Y.~Ye.
\newblock On homogeneous and self--dual algorithms for {LCP}.
\newblock {\em Mathematical Programming}, 76:211--221, 1997.

\bibitem{ipm:Ye65}
Y.~Ye.
\newblock Approximating global quadratic optimization with convex quadratic
  constraints.
\newblock {Working Paper}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, July 1998.

\bibitem{ipm:Ye58}
Y.~Ye.
\newblock On the complexity of approximating a {KKT} point of quadratic
  programming.
\newblock {\em Mathematical Programming}, 80:195--211, 1998.

\bibitem{ipm:Ye62}
Y.~Ye.
\newblock Approximating quadratic programming with quadratic constraints.
\newblock {\em Mathematical Programming}, 84:219--226, 1999.

\bibitem{ipm:Ye51}
Y.~Ye and K.~M. Anstreicher.
\newblock On quadratic and ${O(\sqrt{n} L)}$ convergence of a
  predictor--corrector algorithm for {LCP}.
\newblock {\em Mathematical Programming}, 62:537--551, 1993.

\bibitem{ipm:Ye36}
Y.~Ye and S.~S. Chiu.
\newblock Recovering the shadow price in projection methods for linear
  programming.
\newblock {Technical Report}, Department of Management Science, University of
  Iowa, Iowa City, IA~52242, USA, 1985.

\bibitem{ipm:Ye43}
Y.~Ye, O.~G{\"u}ler, R.~A. Tapia, and Y.~Zhang.
\newblock A quadratically convergent ${O(\sqrt{n}L)}$--iteration algorithm for
  linear programming.
\newblock {\em Mathematical Programming}, 59:151--162, 1993.

\bibitem{ipm:Ye47}
Y.~Ye and J.~A. Kaliski.
\newblock Further results on build--up approaches for linear programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in, Anaheim, CA,
  USA}, Department of Management Science, University of Iowa, Iowa City,
  IA~52242, USA, November 1991.

\bibitem{ipm:Ye20}
Y.~Ye and M.~Kojima.
\newblock Recovering optimal dual solutions in {Karmarkar's} polynomial
  algorithm for linear programming.
\newblock {\em Mathematical Programming}, 39:305--317, 1987.

\bibitem{ipm:Ye42}
Y.~Ye, K.~O. Kortanek, J.~A. Kaliski, and S.~Huang.
\newblock Near--boundary behavior of primal--dual potential reduction
  algorithms for linear programming.
\newblock {\em Mathematical Programming}, 58:243--255, 1993.

\bibitem{ipm:Ye21}
Y.~Ye and P.~M. Pardalos.
\newblock A class of linear complementarity problems solvable in polynomial
  time.
\newblock {\em Linear Algebra and Its Applications}, 152:3--17, 1991.

\bibitem{ipm:Ye37}
Y.~Ye and F.~A. Potra.
\newblock An interior--point algorithm for solving entropy optimization
  problems with globally linear and locally quadratic convergence rate.
\newblock {Working Paper Series} 90--22, Department of Management Science,
  University of Iowa, Iowa City, IA~52242, USA, 1990.
\newblock Same as Potra and Ye \cite{ipm:Potra5}.

\bibitem{ipm:Ye44}
Y.~Ye, R.~A. Tapia, and Y.~Zhang.
\newblock A superlinearly convergent ${O(\sqrt{n}L)}$--iteration algorithm for
  linear programming.
\newblock {Technical Report} TR--91--22, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Ye22}
Y.~Ye and M.~J. Todd.
\newblock Containing and shrinking ellipsoids in the path--following algorithm.
\newblock {\em Mathematical Programming}, 47:1--10, 1990.

\bibitem{ipm:Ye55}
Y.~Ye, M.~J. Todd, and S.~Mizuno.
\newblock An {$O(\sqrt{n} L)$}--iteration homogeneous and self--dual linear
  programming algorithm.
\newblock {\em Mathematics of Operations Research}, 19:53--67, 1994.

\bibitem{ipm:Ye23}
Y.~Ye and E.~Tse.
\newblock A polynomial--time algorithm for convex quadratic programming.
\newblock {Working Paper}, Department of Engineering Economic Systems, Stanford
  University, Stanford, CA~94305, USA, 1986.

\bibitem{ipm:Ye24}
Y.~Ye and E.~Tse.
\newblock An extension of {Karmarkar's} projective algorithm for convex
  quadratic programming.
\newblock {\em Mathematical Programming}, 44:157--179, 1989.

\bibitem{ipm:Yeh1}
Q.~J. Yeh.
\newblock {\em A reduced dual affine scaling algorithm for solving assignment
  and transportation problems}.
\newblock PhD thesis, Department of Industrial Engineering and Operations
  Research, Columbia University, New York, NY~10027, USA, 1989.

\bibitem{ipm:Yen1}
S.~D. Yen and W.~S. Levine.
\newblock Mixed {$H_{2H}$} infinity optimization\,: {A BMI} solution.
\newblock {\em Proceedings of the 1997 36th IEEE Conference on Decision and
  Control}, Part\,1/5:460--465, 1997.

\bibitem{ipm:Yoshise1}
A.~Yoshise.
\newblock An optimization method for convex programming problems -- the
  interior point method and analytical center.
\newblock {\em Systems Control and Informations}, 38:155--160, 1994.
\newblock (In Japanese).

\bibitem{ipm:Yoshise2}
A.~Yoshise.
\newblock Complementarity problems.
\newblock In T.~Terlaky, editor, {\em Interior Point Methods of Mathematical
  Programming}, volume~5 of {\em Applied Optimization}, pages 297--367. Kluer
  Academic Publishers, Dordrecht, The Netherlands, 1996.

\bibitem{ipm:Yuguo1}
H.~Yuguo, L.~Guangyi, and Y.~Erkeng.
\newblock A new {OPF} (optimal power flow) algorithm based on {Karmarkar's}
  interior point method.
\newblock {\em Proceedings of the Chinese Society of Electrical Engineering},
  16:409--412, 1996.
\newblock (In Chinese).

\bibitem{ipm:Yun1}
Z.~G. Yun.
\newblock High--order large--step interior--point algorithms for linear
  complementarity problems.
\newblock {Research Report} 650, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1994.
\newblock Identical to Zhao\,\cite{ipm:Zhao9}.

\bibitem{ipm:Yun2}
Z.~G. Yun and Z.~W. Liu.
\newblock A line--search method for {Lagrangian} relexation ascent algorithms.
\newblock {Research Report} 644, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1994.
\newblock Identical to Zhao and Liu\,\cite{ipm:Zhao10}.

\bibitem{ipm:Zaijan1}
D.~Zaijan.
\newblock A modified {Karmarkar's} algorithm.
\newblock {\em Applied Mathematics---A Journal of Chinese Universities},
  3:41--56, 1988.

\bibitem{ipm:Zaporozhan1}
D.~I. Zaporozhan.
\newblock Exact shifts of the constraints in methods of centers.
\newblock {\em Akademiya Nauk Respubliki Moldova Izvestiya Matematika}, pages
  72--86, 100, 103, 1993.

\bibitem{ipm:Zenios1}
S.~A. Zenios and R.~Qi.
\newblock Data--level parallel computing with interior point algorithms.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Orlando, FL,
  USA}, Department of Decision Sciences, The Wharton School, University of
  Pennsylvania, Philadelphia, PA~19104, USA, April 1992.
\newblock See Eckstein et al.\ \cite{ipm:Eckstein1}.

\bibitem{ipm:Zenios2}
S.~A. Zenios and D.~Yang.
\newblock Massively parallel solution of robust optimization programs via
  interior point algorithms.
\newblock {Talk held at the INFORMS Joint National Meeting in Los Angeles, CA,
  USA}, Department of Decision Sciences, The Wharton School, University of
  Pennsylvania, Philadelphia, PA~19104, USA, April 1995.

\bibitem{ipm:Zhadan1}
V.~G. Zhadan.
\newblock Dual barrier--projection and barrier--{Newton} methods in linear
  programming.
\newblock In J.~Dolezal et~al., editor, {\em System Modelling and Optimization
  (Proceedings of the 17th IFIP Conference, Prague, Czech Republic, July
  1995)}, pages 501--509. Chapman \& Hall, London, Great Britain, 1996.

\bibitem{ipm:Zhang14}
D.~Zhang and Y.~Zhang.
\newblock An infeasible--interior--point algorithm with polynomiality and
  {$Q$}--subcubic convergence.
\newblock {Research Report} 93--13, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA, July
  1993.

\bibitem{ipm:Zhang17}
D.~Zhang and Y.~Zhang.
\newblock A {Mehrotra}--type predictor--corrector algorithm with polynomiality
  and {Q}--subquadratic convergence.
\newblock {\em Annals of Operations Research}, 62:131--150, 1996.

\bibitem{ipm:Zhang6}
J.~Z. Zhang.
\newblock The affine transformation method and the path following method for
  solving linear programming problems.
\newblock {\em Chinese Journal of Operations Research}, 8(2):25--34, 1989.
\newblock (In Chinese).

\bibitem{ipm:Zhang4}
S.~Zhang.
\newblock On the convergence property of {Iri--Imai's} method for linear
  programming.
\newblock {Technical Report} 8917/A, Economic Institute, Erasmus University,
  Rotterdam, The Netherlands, 1989.
\newblock See also Zhang \cite{ipm:SZhang1}.

\bibitem{ipm:SZhang1}
S.~Zhang.
\newblock The convergence property of the {Iri--Imai} algorithm for some smooth
  convex programming problems.
\newblock {\em Journal of Optimization Theory and Applications}, 82:121--138,
  1994.
\newblock See also Zhang \cite{ipm:Zhang4}.

\bibitem{ipm:SZhang2}
S.~Zhang and M.~Shi.
\newblock On the polynomiality of {Iri and Imai's} new algorithm for linear
  programming.
\newblock {\em Journal of Qinhua University}, 28:121--126, 1988.
\newblock (In Chinese).

\bibitem{ipm:Zhang21}
X.~Zhang and K.-C. Zhang.
\newblock A homotopy interior algorithm for posynomial geometric programming.
\newblock {\em Mathematica Numerica Sinica}, 18:225--232, 1996.
\newblock (In Chinese).

\bibitem{ipm:Zhang20}
X.~Zhang and J.~Zhou.
\newblock Interior point method for solving optimization problems.
\newblock {\em Proceedings of the International Conference on Intelligent
  Manufacturing (Wuhan, China, 1995)}, pages 149--155, 1995.

\bibitem{ipm:Zhang19}
X.~Zhang, J.~Zhou, and J.~Yu.
\newblock An optimization method based on a primal--dual interior point
  quadratic programming approach.
\newblock {\em Journal of the Huazhong University of Science and Technology},
  23(9):1--5, 1995.
\newblock (In Chinese).

\bibitem{ipm:Zhang5}
Y.~Zhang.
\newblock Super--linear convergence of interior point algorithms for a class of
  mathematical programming problems.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Nashville,
  Tennessee, USA}, Department of Mathematics \& Statistics, University of
  Maryland Baltimore County, Baltimore, MD~21228, USA, May 1991.

\bibitem{ipm:Zhang12}
Y.~Zhang.
\newblock A primal--dual interior point approach for computing the $\ell_{1}$
  and $\ell_{\infty}$ solutions of overdetermined linear systems.
\newblock {\em Journal of Optimization Theory and Applications},
  77(2):323--341, 1993.

\bibitem{ipm:Zhang23}
Y.~Zhang.
\newblock {LIPSOL -- A MATLAB} toolkit for linear programming interior--point
  solvers.
\newblock {Technical Report}, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA,
  1994.
\newblock See also Zhang \cite{ipm:Zhang23}.

\bibitem{ipm:Zhang11}
Y.~Zhang.
\newblock On the convergence of a class of infeasible interior--point methods
  for the horizontal linear complementarity problem.
\newblock {\em SIAM Journal on Optimization}, 4:208--227, 1994.

\bibitem{ipm:Zhang22}
Y.~Zhang.
\newblock User's guide to {LIPSOL}.
\newblock {Technical Report}, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA, July
  1995.
\newblock See also Zhang \cite{ipm:Zhang24}.

\bibitem{ipm:Zhang18}
Y.~Zhang.
\newblock Solving large--scale linear programs by interior--point methods under
  the {MATLAB} environment.
\newblock {Technical Report} 96--01, Department of Mathematics and Statistics,
  University of Maryland Baltimore County, Baltimore, MD~21228--5398, USA,
  March 1996.

\bibitem{ipm:Zhang16}
Y.~Zhang.
\newblock On extending primal--dual interior--point algorithms from linear
  programming to semidefinite programming.
\newblock {\em SIAM Journal on Optimization}, 8:365--386, 1998.

\bibitem{ipm:Zhang10}
Y.~Zhang and A.~S. El-Bakry.
\newblock A modified predictor--corrector algorithm for locating weighted
  centers in linear programming.
\newblock {\em Journal of Optimization Theory and Applications}, 80:319--331,
  1994.

\bibitem{ipm:Zhang7}
Y.~Zhang and R.~A. Tapia.
\newblock A quadratically convergent polynomial primal--dual interior--point
  algorithm for linear programming.
\newblock {Technical Report} TR~90--40, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1990.
\newblock To appear in {\em SIAM Journal on Optimization 3 (1993)}.

\bibitem{ipm:Zhang9}
Y.~Zhang and R.~A. Tapia.
\newblock On the convergence of interior--point methods to the center of the
  solution set in linear programming.
\newblock {Technical Report} TR~91--30, Department of Mathematical Sciences,
  Rice University, Houston, TX~77251, USA, 1991.

\bibitem{ipm:Zhang3}
Y.~Zhang and R.~A. Tapia.
\newblock A polynomial--time and superlinearly convergent interior point
  algorithm for linear programming.
\newblock {Technical Report}, Department of Mathematical Sciences, Rice
  University, Houston, TX~77251, USA, March 1991.
\newblock To appear in {\em SIAM Journal on Optimization, 1992}.

\bibitem{ipm:Zhang8}
Y.~Zhang and R.~A. Tapia.
\newblock Superlinear and quadratic convergence of primal--dual interior--point
  methods for linear programming revisited.
\newblock {\em Journal of Optimization Theory and Applications},
  73(2):229--242, 1992.

\bibitem{ipm:Zhang1}
Y.~Zhang, R.~A. Tapia, and J.~E. Dennis.
\newblock On the superlinear and quadratic convergence of primal--dual interior
  point linear programming algorithms.
\newblock {\em SIAM Journal on Optimization}, 2(2):304--324, 1992.

\bibitem{ipm:Zhang2}
Y.~Zhang, R.~A. Tapia, and F.~Potra.
\newblock On the superlinear convergence of interior point algorithms for a
  general class of problems.
\newblock {\em SIAM Journal on Optimization}, 3(2):413--422, 1993.

\bibitem{ipm:Zhang13}
Y.~Zhang and D.~Zhang.
\newblock Superlinear convergence of infeasible interior--point methods for
  linear programming.
\newblock {\em Mathematical Programming}, 66:361--377, 1994.

\bibitem{ipm:Zhang15}
Y.~Zhang and D.~Zhang.
\newblock On polynomiality of the {Mehrotra}--type predictor--corrector
  interior--point algorithm.
\newblock {\em Mathematical Programming}, 68:303--318, 1995.

\bibitem{ipm:Zhao6}
G.~Y. Zhao.
\newblock {\em Estimating the complexity of path--following methods in linear
  programming by curvature integrals along the central trajectory}.
\newblock PhD thesis, Institut f{\"u}r Angewandte Mathematik und Statistik,
  Universit{\"a}t W{\"u}rzburg, Am Hubland, D--97074~W{\"u}rzburg, Germany,
  1991.

\bibitem{ipm:Zhao11}
G.~Y. Zhao.
\newblock Large--step path--following primal--dual algorithms for linear
  programming.
\newblock {Research Report} 613, Department of Mathematics, National University
  of Singapore, Singapore~0511, March 1994.

\bibitem{ipm:Zhao9}
G.~Y. Zhao.
\newblock High--order large--step interior point algorithms for linear
  complementary problems.
\newblock {Research Report} 650, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1995.
\newblock Identical to Yun\,\cite{ipm:Yun1}.

\bibitem{ipm:Zhao7}
G.~Y. Zhao.
\newblock On the choice of parameters for power--series interior point
  algorithms in linear programming.
\newblock {\em Mathematical Programming}, 68:49--71, 1995.

\bibitem{ipm:Zhao15}
G.~Y. Zhao.
\newblock Interior point methods with decomposition for linear programs.
\newblock {Research Report} 686, Department of Mathematics, National University
  of Singapore, Singapore~0511, 1996.

\bibitem{ipm:Zhao3}
G.~Y. Zhao.
\newblock Relationship between the curvature integral and the complexity of
  path--following methods in linear programming.
\newblock {\em SIAM Journal on Optimization}, 6:57--73, 1996.

\bibitem{ipm:Zhao13}
G.~Y. Zhao.
\newblock Log--barrier decomposition methods for solving two--stage stochastic
  programs.
\newblock {Research Report} 711, Department of Mathematics, National University
  of Singapore, Singapore~0511, June 1997.
\newblock Revised June 1998.

\bibitem{ipm:Zhao16}
G.~Y. Zhao.
\newblock Barrier function in the {Lagrangian} dual method for solving
  multi--stage stochastic nonlinear programs.
\newblock {Research Report}, Department of Mathematics, National University of
  Singapore, Singapore~0511, 1998.

\bibitem{ipm:Zhao12}
G.~Y. Zhao.
\newblock Interior point algorithms for linear complementarity problems based
  on large neighborhoods of the central path.
\newblock {\em SIAM Journal on Optimization}, 8:397--413, 1998.

\bibitem{ipm:Zhao10}
G.~Y. Zhao and Z.~W. Liu.
\newblock A line search method for {Lagrangian} relaxation ascent algorithms.
\newblock {Technical Report} 644, Department of Mathematics, National
  University of Singapore, Singapore~0511, 1995.
\newblock Identical to Yun and Liu\,\cite{ipm:Yun2}.

\bibitem{ipm:Zhao1}
G.~Y. Zhao and J.~Stoer.
\newblock Estimating the complexity of path--following methods for solving
  linear programs by curvature integrals.
\newblock {\em Applied Mathematics~{\&}~Optimization}, 27(1):85--103, 1993.

\bibitem{ipm:Zhao14}
G.~Y. Zhao and J.~Sun.
\newblock On the rate of local convergence of higher--order
  infeasible--path--following algorithms for {$P_{*}$--LCP with or without
  strictly complementary solutions}.
\newblock {Research Report} 698, Department of Mathematics, National University
  of Singapore, Singapore~0511, March 1997.

\bibitem{ipm:Zhao8}
G.~Y. Zhao, J.~Sun, and J.~Zhu.
\newblock A primal--dual affine scaling algorithm with necessary centering as a
  safeguard.
\newblock {\em Optimization}, 35:333--343, 1995.

\bibitem{ipm:Zhao5}
G.~Y. Zhao and J.~Zhu.
\newblock Analytical properties of the central trajectory in interior point
  methods.
\newblock In D.-Z. Du and J.~Sun, editors, {\em Advances in Optimization and
  Approximation}, volume~1 of {\em Nonconvex Optimization and Its
  Applications}, pages 362--375. Kluwer Academic Publishers, Dordrecht, The
  Netherlands, 1994.

\bibitem{ipm:Zhao4}
G.~Y. Zhao and J.~Zhu.
\newblock The curvature integral and the complexity of linear complementarity
  problems.
\newblock {\em Mathematical Programming}, 70:107--122, 1995.

\bibitem{ipm:Zhao2}
Y.~Zhao.
\newblock A classification of trajectory optimization algorithms.
\newblock {Technical Report} 91/115, Minnesota Supercomputer Institute,
  University of Minnesota, Minneapolis, MN~55415, USA, April 1991.

\bibitem{ipm:Zheng1}
Q.~Zheng.
\newblock On the complexity of linear programming problems.
\newblock {\em Chinese Journal of Operations Research}, 7(2):1--10, 1988.
\newblock (In Chinese).

\bibitem{ipm:Zhou1}
J.~Zhou, N.~Xu, and W.~Chen.
\newblock Discussion on {Karmarkar's} method for solving unstandard model.
\newblock {\em Journal of Southeastern University (Nanjing, PR China), English
  Edition}, 5(1):38--45, 1989.

\bibitem{ipm:Zhu2}
J.~Zhu.
\newblock A path following algorithm for a class of convex programming
  problems.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 36(4):539--377, 1992.

\bibitem{ipm:Zhu3}
J.~Zhu and S.~Huang.
\newblock On the convergence rate of the duality gap in a symmetric
  primal--dual potential reduction algorithm.
\newblock {\em Operations Research Letters}, 11:289--291, 1992.

\bibitem{ipm:Zhu1}
J.~Zhu and K.~O. Kortanek.
\newblock A polynomial path--following algorithm for linearly constrained
  convex programming.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Philadelphia,
  PA, USA}, College of Business Administration, University of Iowa, Iowa City,
  IA~52240, USA, October 1990.

\bibitem{ipm:Zikan1}
K.~Zikan and R.~W. Cottle.
\newblock The box method for linear programming, {Part\,I\,: Basic} theory.
\newblock {Technical Report}, Systems Optimization Laboratory, Department of
  Operations Research, Stanford University, Stanford, CA~94305--4022, USA,
  1987.

\bibitem{ipm:Zikan2}
K.~Zikan and R.~W. Cottle.
\newblock The box method for linear programming, {Part\,II\,: Treatment} of
  problems in standard form with explicitly bounded variables.
\newblock {Technical Report}, Systems Optimization Laboratory, Department of
  Operations Research, Stanford University, Stanford, CA~94305--4022, USA,
  1987.

\bibitem{ipm:Zikan3}
K.~Zikan and R.~W. Cottle.
\newblock Solving linear programs with the box method.
\newblock {Talk held at the ORSA/TIMS Joint National Meeting in Washington, DC,
  USA}, Systems Optimization Laboratory, Department of Operations Research,
  Stanford University, Stanford, CA~94305--4022, USA, April 1988.

\bibitem{ipm:Zimmermann1}
U.~Zimmermann.
\newblock On recent developments in linear programming.
\newblock In K.~H. Hoffmann, J.~B. Hiriat-Urruty, C.~Lemarechal, and J.~Zowe,
  editors, {\em Trends in Mathematical Optimization\,: Proceedings of the 4th
  French--German Conference on Optimization in Irsee, Germany, April 1986},
  volume~84 of {\em International Series of Numerical Mathematics}, pages
  353--390. Birkh{\"a}user Verlag, Basel, Switzerland, 1988.

\bibitem{ipm:Zimmermann2}
U.~Zimmermann.
\newblock Search directions for projective methods.
\newblock {Technical Report}, Technische Universit{\"a}t Braunschweig, Institut
  f{\"u}r Angewandte Mathematik, Abt.\ f{\"u}r Math.\ Optimierung,
  Pockelstr.~14, D--3300~Braunschweig, Germany, February 1989.

\bibitem{ipm:Zimmermann3}
U.~Zimmermann.
\newblock Search directions for a class of projective methods.
\newblock {\em Zeitschrift f{\"u}r Operations Research---Methods and Models of
  Operations Research}, 34:353--379, 1990.

\bibitem{ipm:Zimmermann4}
U.~Zimmermann and C.~Wallacher.
\newblock An interior point method for flow problems.
\newblock {Talk held at the DGOR--Jahrestagung in Vienna, Austria}, Technische
  Universit{\"a}t Braunschweig, Institut f{\"u}r Angewandte Mathematik, Abt.\
  f{\"u}r Math.\ Optimierung, Pockelstr.~14, D--3300~Braunschweig, Germany,
  August 1990.
\newblock See also Wallacher and Zimmermann \cite{ipm:Wallacher1}.

\end{thebibliography}