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

Variable x(i) , obj  ;
Equation c1 , c2 , c3 , c4 , Def_obj ;

c1..  2*sqr(x['i1']) + 3*power(x['i2'],4) + x['i3'] + 4*sqr(x['i4']) + 5*x['i5'] =l= 127;
c2..      7*x['i1'] +        3*x['i2']    + 10*sqr(x['i3']) + x['i4'] - x['i5'] =l=282;
c3..     23*x['i1'] +      sqr(x['i2'])   + 6*sqr(x['i6']) - 8*x['i7'] =l= 196;
c4.. -4*sqr(x['i1']) -     sqr(x['i2'])   + 3*x['i1']*x['i2'] -2*sqr(x['i3']) -5*x['i6']+11*x['i7'] =g= 0;

Def_obj.. obj =e=   sqr(x['i1']-10)    + 5*sqr(x['i2']-12) +
                    sqr(sqr(x['i3']))  + 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;

* "optimal solution as starting point ";
*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 hs100 /all/ ;
Solve hs100 using nlp minimazing obj ;
obj.l = obj.l - 680.6300573;
display obj.l;