* Shitkovski AMPL model  (translation to GAMS)

Set I /1,2/;

Variable  x[I],Obj;

Equation Eq_1,Eq_2,Eq_3,Def_obj;

Def_obj.. Obj =e= 100*sqr(x['2'] - sqr(x['1'])) + sqr(1-x['1']);

Eq_1..              x['1'] + sqr(x['2']) =g= 0;
Eq_2..              sqr(x['1']) + x['2'] =g= 0;
Eq_3..              sqr(x['1']) + sqr(x['2']) =g= 1;

x.lo['1'] = -1/2 ;
x.up['1'] =  1/2 ;

x.l['1'] =  -0;
x.l['2'] =   0;

* "optimal solution as starting point \n";
*x.l['1'] =  1/2;
*x.l['2'] =  1/(2*sqrt(3));

Model hs020 /all/;
Solve hs020 using nlp minimaze obj;

display x.l  ;
display obj.l;
parameter a; a= -(-81.5+25*sqrt(3));
display a    ;

*optimal obj =  -(-81.5+25*sqrt(3));