$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,i3,i4,i5,i6,objvar;

Integer Variables i1,i2,i3,i4,i5,i6;

Equations  e1,e2,e3,e4,e5,e6,e7;


e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2 - 7*
     sqr(i4) - 10*i4*i1 - 6*i4*i2 - 2*i4*i3 - 2*i5*i2 - 7*sqr(i5) - 6*i6*i1 - 2
     *i6*i2 - 2*i6*i4 - 5*sqr(i6) =G= -1800;

e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2 - 8*
     sqr(i4) + 2*i4*i1 + 10*i4*i2 - 2*i5*i1 - 6*i5*i2 + 6*i5*i4 + 7*sqr(i5) - 2
     *i6*i2 + 8*i6*i3 + 2*i6*i4 - 4*i6*i5 - 8*sqr(i6) =G= -1520;

e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 - 6*sqr(i4) + 4*
     i4*i1 + 4*i4*i2 - 2*i4*i3 - 6*i5*i1 - 2*i5*i2 + 4*i5*i4 + 6*sqr(i5) + 2*i6
     *i1 + 4*i6*i2 - 6*i6*i4 - 2*i6*i5 - 5*sqr(i6) =G= -1000;

e4.. (-8*sqr(i1)) - 4*sqr(i2) - 9*sqr(i3) - 7*sqr(i4) - 2*i2*i1 - 2*i3*i1 - 4*
     i3*i2 + 6*i4*i1 + 2*i4*i2 - 2*i4*i3 - 6*i5*i1 - 4*i5*i2 - 2*i5*i3 + 6*i5*
     i4 + 6*sqr(i5) - 10*i6*i1 - 10*i6*i3 + 4*i6*i4 - 2*i6*i5 - 7*sqr(i6)
      =G= -1745;

e5.. 2*i2*i1 - 4*sqr(i1) - 5*sqr(i2) - 6*i3*i1 - 8*sqr(i3) - 2*i4*i1 + 6*i4*i2
      - 2*i4*i3 - 6*sqr(i4) - 4*i5*i1 + 2*i5*i2 - 6*i5*i3 - 8*i5*i4 - 7*sqr(i5)
      + 4*i6*i1 - 4*i6*i2 + 6*i6*i3 + 4*i6*i5 - 7*sqr(i6) =G= -1070;

e6.. 2*i2*i1 - 7*sqr(i1) - 7*sqr(i2) - 6*i3*i1 - 2*i3*i2 - 6*sqr(i3) - 2*i4*i1
      + 2*i4*i2 - 2*i4*i3 - 5*sqr(i4) - 2*i5*i1 - 4*i5*i3 + 2*i5*i4 - 5*sqr(i5)
      + 2*i6*i1 - 4*i6*i2 + 4*i6*i3 + 2*i6*i4 + 6*i6*i5 - 9*sqr(i6) =G= -990;

e7..  - (7*sqr(i1) + 6*sqr(i2) + 0.2*i1 - 53.6*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*
     i2 + 4.4*i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 24.8*i4 + 7*sqr(i5) - 4*i5*
     i1 - 2*i5*i2 - 6*i5*i3 - 104.8*i5 + 4*sqr(i6) + 2*i6*i1 - 4*i6*i2 - 4*i6*
     i3 - 2*i6*i4 + 6*i6*i5 - 56.4*i6) + objvar =E= 0;

* set non default bounds

i1.up = 200; 
i2.up = 200; 
i3.up = 200; 
i4.up = 200; 
i5.up = 200; 
i6.up = 200; 

* set non default levels

i1.l = 1; 
i2.l = 1; 
i3.l = 1; 
i4.l = 1; 
i5.l = 1; 
i6.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;