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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,i4,i5,i6,i7,i8,i9,i10,objvar;

Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10;

Equations  e1;


e1..  - (sqr(log(i1 - 2)) + sqr(log(10 - i1)) + sqr(log(i2 - 2)) + sqr(log(10
      - i2)) + sqr(log(i3 - 2)) + sqr(log(10 - i3)) + sqr(log(i4 - 2)) + sqr(
     log(10 - i4)) + sqr(log(i5 - 2)) + sqr(log(10 - i5)) + sqr(log(i6 - 2)) + 
     sqr(log(10 - i6)) + sqr(log(i7 - 2)) + sqr(log(10 - i7)) + sqr(log(i8 - 2)
     ) + sqr(log(10 - i8)) + sqr(log(i9 - 2)) + sqr(log(10 - i9)) + sqr(log(i10
      - 2)) + sqr(log(10 - i10)) - (i1*i2*i3*i4*i5*i6*i7*i8*i9*i10)**0.2)
      + objvar =E= 0;

* set non default bounds

i1.lo = 3; i1.up = 9; 
i2.lo = 3; i2.up = 9; 
i3.lo = 3; i3.up = 9; 
i4.lo = 3; i4.up = 9; 
i5.lo = 3; i5.up = 9; 
i6.lo = 3; i6.up = 9; 
i7.lo = 3; i7.up = 9; 
i8.lo = 3; i8.up = 9; 
i9.lo = 3; i9.up = 9; 
i10.lo = 3; i10.up = 9; 

* set non default levels

i1.l = 5; 
i2.l = 5; 
i3.l = 5; 
i4.l = 5; 
i5.l = 5; 
i6.l = 5; 
i7.l = 5; 
i8.l = 5; 
i9.l = 5; 
i10.l = 5; 

* 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;