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## nvs09.gms:

#### References:

• Tawarmalani, M, and Sahinidis, N, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, P M, and Romeijn, E, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches. Kluwer Academic Publishers, 2001.
• Gupta, O K, and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming. Management Science 13 (1985), 1533-1546.

Point: p1
Best known point (p1): Solution value -43.13 (global optimum, LINDOGLOBAL certificate)

\$offlisting * MINLP written by GAMS Convert at 07/24/02 13:01:21 * * Equation counts * Total E G L N X C * 1 1 0 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 11 1 0 10 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 11 1 10 0 * * Solve m using MINLP minimizing objvar; 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; \$if set nostart \$goto modeldef * 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 \$label modeldef Model m / all /; m.limrow=0; m.limcol=0; \$if NOT '%gams.u1%' == '' \$include '%gams.u1%' \$if not set MINLP \$set MINLP MINLP Solve m using %MINLP% minimizing objvar;