# hs105.mod	OBR2-RN-8-16
# Original AMPL coding by Elena Bobrovnikova (summer 1996 at Bell Labs).

# Maximum likelihood estimation

# Ref.: W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming
# Codes.  Lecture Notes in Economics and Mathematical Systems, v. 187,
# Springer-Verlag, New York, 1981, p. 114.

# Number of variables:  8
# Number of constraints:  16 (17 before presolve)
# Objective nonseparable
# Objective nonconvex
# Linear constraints

set I := 1 .. 235;

param PI := 4*atan(1);
param y{I};

var x{1..8};
var a{i in I} = x[1] / x[6] * exp(-(y[i] - x[3])^2 / (2 * x[6]^2));
var b{i in I} = x[2] / x[7] * exp(-(y[i] - x[4])^2 / (2 * x[7]^2));
var c{i in I} = (1 - x[2] - x[1]) / x[8] *
                   exp(-(y[i] - x[5])^2 / (2 * x[8]^2));

minimize f:
      - sum {i in I} log((a[i] + b[i] + c[i]) / sqrt(2 * PI));

s.t. C1:
     1 - x[1] - x[2] >= 0;
s.t. B12{i in 1..2}:
     .001 <= x[i] <= .499;
s.t. B3:
     100 <= x[3] <= 180;
s.t. B4:
     130 <= x[4] <= 210;
s.t. B5:
     170 <= x[5] <= 240;
s.t. B678{i in 6..8}:
     5 <= x[i] <= 25;


data;

param   y :=
        1     95     61     135      121    155      181   180
        2    105     62     135      122    155      182   185
        3    110     63     135      123    160      183   185
        4    110     64     135      124    160      184   185
        5    110     65     135      125    160      185   185
        6    110     66     135      126    160      186   185
        7    115     67     135      127    160      187   185
        8    115     68     135      128    160      188   190
        9    115     69     140      129    160      189   190
       10    115     70     140      130    160      190   190
       11    120     71     140      131    160      191   190
       12    120     72     140      132    160      192   190
       13    120     73     140      133    160      193   190
       14    120     74     140      134    160      194   190
       15    120     75     140      135    160      195   195
       16    120     76     140      136    160      196   195
       17    120     77     140      137    160      197   195
       18    120     78     140      138    160      198   195
       19    120     79     140      139    160      199   200
       20    120     80     140      140    160      200   200
       21    120     81     140      141    160      201   200
       22    120     82     140      142    160      202   205
       23    120     83     140      143    165      203   205
       24    120     84     140      144    165      204   205
       25    120     85     140      145    165      205   210
       26    125     86     140      146    165      206   210
       27    125     87     140      147    165      207   210
       28    125     88     140      148    165      208   210
       29    125     89     140      149    165      209   210
       30    125     90     145      150    165      210   210
       31    125     91     145      151    170      211   210
       32    125     92     145      152    170      212   210
       33    125     93     145      153    170      213   215
       34    125     94     145      154    170      214   220
       35    125     95     145      155    170      215   220
       36    125     96     145      156    170      216   220
       37    125     97     145      157    170      217   220
       38    125     98     145      158    170      218   220
       39    125     99     145      159    170      219   220
       40    125    100     145      160    170      220   230
       41    130    101     145      161    170      221   230
       42    130    102     150      162    170      222   230
       43    130    103     150      163    170      223   230
       44    130    104     150      164    170      224   230
       45    130    105     150      165    170      225   235
       46    130    106     150      166    170      226   240
       47    130    107     150      167    170      227   240
       48    130    108     150      168    175      228   240
       49    130    109     150      169    175      229   240
       50    130    110     150      170    175      230   240
       51    130    111     150      171    175      231   240
       52    130    112     150      172    175      232   240
       53    130    113     150      173    175      233   245
       54    130    114     150      174    175      234   250
       55    130    115     150      175    175      235   250
       56    135    116     150      176    180
       57    135    117     150      177    180
       58    135    118     150      178    180
       59    135    119     155      179    180
       60    135    120     155      180    180                 ;


var x :=
    1   .1
    2   .2
    3   100
    4   125
    5   175
    6   11.2
    7   13.2
    8   15.8  ;