$ontext

Purpose: To provide a GAMS formulation for the collection
of Gupta Problems

Reference: Branch and bound experiments in convex nonlinear
integer programming, Management Science, 1533-1546, 31, 1985.

$offtext

Variables  i1,i2,x3,objvar;

Integer Variables i1,i2;

Equations  e1,e2,e3,e4;


e1.. sqrt(x3) + i1 + 2*i2 =G= 10;

e2.. 0.240038406144983*sqr(i1) - i2 + 0.255036980362153*x3 =G= -3;

e3.. sqr(i2) - 1/(POWER(x3,3)*sqrt(x3)) - 4*i1 =G= -12;

e4..  - (sqr(i1 - 3) + sqr(i2 - 2) + sqr(4 + x3)) + objvar =E= 0;

* set non default bounds

i1.up = 200; 
i2.up = 200; 
x3.lo = 0.001; x3.up = 200; 

* set non default levels

i1.l = 1; 
i2.l = 1; 
x3.l = 1; 

* set non default marginals


Model m / all /;

m.limrow=0; m.limcol=0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

Solve m using MINLP minimizing objvar;