* Cute AMPL model  (translation to GAMS)
*
* AMPL Model by Hande Y. Benson
*
* Copyright (C) 2001 Princeton University
* All Rights Reserved
*
* Permission to use, copy, modify, and distribute this software and
* its documentation for any purpose and without fee is hereby
* granted, provided that the above copyright notice appear in all
* copies and that the copyright notice and this
* permission notice appear in all supporting documentation.

*   Source: a modification by Ph. Toint of problem 100 in
*   W. Hock and K. Schittkowski,
*   "Test examples for nonlinear programming codes",
*   Lectures Notes in Economics and Mathematical Systems 187, Springer
*   Verlag, Heidelberg, 1981.

*   SIF input: Ph. Toint, April 1991.

*   classification OOR2-AN-7-4

$Set N 7
Set i /i1*i%N%/;

Variable x[i] ,
          obj ;

Equation constr1    ,
         constr2    ,
         constr3    ,
         constr4    ,
         Def_obj     ;

constr1..  2*sqr(x['i1']) + 3*power(x['i2'],4) +        x['i3']         +
           4*sqr(x['i4']) + 5*x['i5']                                  =l= 127;
constr2..      7*x['i1']  +       3*x['i2']    + 10*sqr(x['i3'])        +
                 x['i4']  -   x['i5']                                  =l= 282;
constr3..     23*x['i1']  +     sqr(x['i2'])   +  6*sqr(x['i6'])        -
               8*x['i7']                                               =l= 196;
constr4.. -4*sqr(x['i1']) -     sqr(x['i2'])   +  3*    x['i1']*x['i2'] -
           2*sqr(x['i3']) -    2193*x['i6']    + 11*x['i7'] +587*x['i4']+
                                                           391*x['i5'] =g=   0;

Def_obj..  obj =e= sqr(x['i1']-10) + 5*sqr(x['i2']-12)   + power(x['i3'],4) +
                 3*sqr(x['i4']-11) + 10*power(x['i5'],6) + 7*sqr(x['i6'])   +
                 power(x['i7'], 4) -   4*x['i6']*x['i7'] - 10*x['i6']       -
                 8*x['i7'] ;
x.l['i1'] = 1;
x.l['i2'] = 2;
x.l['i3'] = 0;
x.l['i4'] = 4;
x.l['i5'] = 0;
x.l['i6'] = 1;
x.l['i7'] = 1;

*printf "optimal solution as starting point \n";
*x.l['i1'] = 2.330499;
*x.l['i2'] = 1.951372;
*x.l['i3'] = -0.4775414;
*x.l['i4'] = 4.365726;
*x.l['i5'] = -0.6244870;
*x.l['i6'] = 1.038131;
*x.l['i7'] = 1.594227;

Model hs100mod  /all/;

Solve hs100mod using nlp minimize obj;

display   x.l               ;

obj.l = obj.l - 680.6300573 ;
display obj.l               ;