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## nvs22.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 6.06 (global optimum, LINDOGLOBAL certificate)

\$offlisting * MINLP written by GAMS Convert at 07/24/02 13:01:19 * * Equation counts * Total E G L N X C * 10 5 5 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 9 5 0 4 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 31 7 24 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,x5,x6,x7,x8,objvar; Integer Variables i1,i2,i3,i4; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10; e1.. - 4243.28147100424/(i3*i4) + x5 =E= 0; e2.. - sqrt(0.25*sqr(i4) + sqr(0.5*i1 + 0.5*i3)) + x7 =E= 0; e3.. - 0.707213578500707*(84000 + 3000*i4)*x7/(i3*i4*(0.0833333333333333*sqr( i4) + sqr(0.5*i1 + 0.5*i3))) + x6 =E= 0; e4.. - 0.5*i4/x7 + x8 =E= 0; e5.. - sqrt(sqr(x5) + 2*x5*x6*x8 + sqr(x6)) =G= -13600; e6.. - 504000/(i2*sqr(i1)) =G= -30000; e7.. i2 - i3 =G= 0; e8.. 0.0204744897959184*sqrt(10000000000000*i1*POWER(i2,3)*i1*POWER(i2,3))*(1 - 0.0282346219657891*i1) =G= 6000; e9.. - 2.1952/(i2*POWER(i1,3)) =G= -0.25; e10.. - (1.10471*i3**2*i4 + 0.04811*i1*i2*(14 + i4)) + objvar =E= 0; * set non default bounds i1.lo = 1; i1.up = 200; i2.lo = 1; i2.up = 200; i3.lo = 1; i3.up = 20; i4.lo = 1; i4.up = 20; \$if set nostart \$goto modeldef * set non default levels i1.l = 2; i2.l = 2; i3.l = 2; i4.l = 2; x5.l = 1; x6.l = 1; x7.l = 1; x8.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;