* 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:
*   B.N. Pshenichnyj
*   "The Linearization Method for Constrained Optimization",
*   Springer Verlag, SCM Series 22, Heidelberg, 1994

*   SIF input: Ph. Toint, December 1994.

*   classification OQR2-AN-2-5

$Set N  20
Set I  / i1*i%N% / ;

$Set M  2
Set j  / j1*j%M% / ;

Parameter  xinit[j] / j1 80.0 , j2 100.0 / ;
Parameter  x_up[j]  / j1 75.0 , j2  65.0 / ;
Parameter b[i] / i1      75.1963666677 ,  i2      -3.8112755343 ,
                 i3       0.1269366345 ,  i4      -0.0020567665 ,
                 i5       0.103450e-4  ,  i6      -6.8306567613 ,
                 i7       0.0302344793 ,  i8      -0.0012813448 ,
                 i9       0.352599e-4  , i10      -0.2266e-6    ,
                i11       0.2564581253 , i12      -0.003460403  ,
                i13       0.135139e-4  , i14     -28.1064434908 ,
                i15      -0.52375e-5   , i16      -0.63e-8      ,
                i17       0.7e-9       , i18      0.0003405462 ,
                i19      -0.16638e-5   , i20      -2.8673112392 /;


Positive Variable x[j] ;

         Variable  f   ;

Equation cons3 , cons4 , cons5 , cons6 ,cons7 , Def_obj ;


cons3..        x['j1']*x['j2']                           -  700.0 =g= 0;
cons4..  0.008*x['j1']*x['j1'] -        x['j2']                   =l= 0;
cons5..  5    *x['j1'] + 100.00*x['j2']- x['j2']*x['j2'] - 2775.0 =l= 0;
cons6..        x['j1'] -   1.50*x['j2']                  -   22.5 =l= 0;
cons7..       -x['j1'] +   0.16*x['j2']                  -   41.4 =l= 0;
Def_obj..
f =e= -b['i2']*x['j1']-b['i6']*x['j2']-b['i1']  -
                   (  b['i3']*power(x['j1'],2) +
                      b['i4']*power(x['j1'],3) +
                      b['i5']*power(x['j1'],4) +x['j2']*(b['i7']*x['j1']+
                      b['i8']*power(x['j1'],2) +
                      b['i9']*power(x['j1'],3) +
                     b['i10']*power(x['j1'],4) ) +
                     b['i11']*power(x['j2'],2) +
                     b['i12']*power(x['j2'],3) +
                     b['i13']*power(x['j2'],4) +
                                    b['i14']/(1+x['j2']) + (b['i18']*x['j1'] +
                     b['i15']*power(x['j1'],2) +
                     b['i16']*power(x['j1'],3))*sqr(x['j2']) + (
                     b['i17']*power(x['j1'],3) +
                     b['i19']*      x['j1'])*power(x['j2'],3)
+                    b['i20']        *exp(0.0005 * x['j1']*x['j2']) );



x.up[j] = x_up[j] ;
x.l[j] = xinit[j] ;

Model himmelp6 /all/ ;

Solve himmelp6 using nlp minimazing f ;

Display x.l ;
Display f.l ;