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## nvs02.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 5.98 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 07/24/02 13:01:19 * * Equation counts * Total E G L N X C * 4 4 0 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 9 4 0 5 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 20 4 16 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,i5,x6,x7,x8,objvar; Positive Variables x6; Integer Variables i1,i2,i3,i4,i5; Equations e1,e2,e3,e4; e1.. - (0.0056858*i2*i5 + 0.0006262*i1*i4 - 0.0022053*i3*i5) + x6 =E= 85.334407; e2.. - (0.0071317*i2*i5 + 0.0029955*i1*i2 + 0.0021813*sqr(i3)) + x7 =E= 80.51249; e3.. - (0.0047026*i3*i5 + 0.0012547*i1*i3 + 0.0019085*i3*i4) + x8 =E= 9.300961; e4.. - 9.99999999999999e-5*(5.3578547*i3**2 + 0.8356891*i1*i5 + 37.293239*i1) + objvar =E= 5.9207859; * set non default bounds i1.up = 200; i2.up = 200; i3.up = 200; i4.up = 200; i5.up = 200; x6.up = 92; x7.lo = 90; x7.up = 110; x8.lo = 20; x8.up = 25; \$if set nostart \$goto modeldef * set non default levels i1.l = 100; i2.l = 100; i3.l = 100; i4.l = 100; i5.l = 100; * 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;