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## nvs11.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 -431.00 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 07/24/02 13:01:13 * * Equation counts * Total E G L N X C * 4 1 3 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 4 1 0 3 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 13 1 12 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,objvar; Integer Variables i1,i2,i3; Equations e1,e2,e3,e4; e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2 =G= -1000; e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2 =G= -550; e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 =G= -340; e4.. - (7*sqr(i1) + 6*sqr(i2) - 15.8*i1 - 93.2*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3 *i2 - 63*i3) + objvar =E= 0; * set non default bounds i1.up = 200; i2.up = 200; i3.up = 200; \$if set nostart \$goto modeldef * set non default levels i1.l = 1; i2.l = 1; i3.l = 1; * 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;