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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.

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Variables  i1,i2,i3,objvar;

Integer Variables i1,i2,i3;

Equations  e1,e2;


e1..  - i1 - i2 - 2*i3 =G= -3;

e2..  - (2*sqr(i1) - 8*i1 + 2*sqr(i2) - 6*i2 + sqr(i3) - 4*i3 + 2*i1*i2 + 2*i1*
     i3) + objvar =E= 9;

* set non default bounds

i1.up = 200; 
i2.up = 200; 
i3.up = 200; 

* set non default levels

i1.l = 100; 
i2.l = 100; 
i3.l = 100; 

* 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;