* Cute AMPL model  (translation to GAMS)
*
$Set N 6
Set i /i1*i%N%/;

parameter u(i)  /i1   0.31  ,i2   0.046 ,i3   0.068 ,
                 i4   0.042 ,i5   0.028 ,i6   0.0134/;

Positive Variable x[i];
         Variable obj ;

Equation constr1 ,
         constr2 ,
         constr3 ,
         constr4 ,
         Def_obj  ;


constr1.. 17.1*x['i1'] + 38.2*x['i2'] + 204.2*x['i3'] +
          212.3*x['i4'] + 623.4*x['i5'] + 1495.5*x['i6'] -
          169*x['i1']*x['i3'] - 3580*x['i3']*x['i5'] -
          3810*x['i4']*x['i5'] - 18500*x['i4']*x['i6'] -
          24300*x['i5']*x['i6'] =g= 32.97;

constr2.. 17.9*x['i1'] + 36.8*x['i2'] + 113.9*x['i3'] +
          169.7*x['i4'] + 337.8*x['i5'] + 1385.2*x['i6'] -
          139*x['i1']*x['i3'] - 2450*x['i4']*x['i5'] -
          16600*x['i4']*x['i6'] - 17200*x['i5']*x['i6'] =g=
          25.12;

constr3..  -273*x['i2'] - 70*x['i4'] - 819*x['i5'] +
          26000*x['i4']*x['i5'] =g= -124.08;

constr4.. 159.9*x['i1'] - 311*x['i2'] + 587*x['i4'] +
          391*x['i5'] + 2198*x['i6'] - 14000*x['i1']*x['i6']=g= -173.02;

Def_obj..  obj =e= 4.3*x['i1'] + 31.8*x['i2'] + 63.3*x['i3'] +
                   15.8*x['i4'] + 68.5*x['i5'] + 4.7*x['i6'] ;

x.up[i]   = u[i];

x.l['i1'] = 0;
x.l['i2'] = 0;
x.l['i3'] = 0;
x.l['i4'] = 0;
x.l['i5'] = 0;
x.l['i6'] = 0;

*printf "optimal solution as starting point \n";
*x.l['i1'] = 0.2685649;
*x.l['i2'] = 0;
*x.l['i3'] = 0;
*x.l['i4'] = 0;
*x.l['i5'] = 0.28;
*x.l['i6'] = 0.0134;


Model hs098  /all/;

Solve hs098 using nlp minimize obj;

display   x.l               ;

obj.l = obj.l  - 3.1358091;
display obj.l               ;