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## nvs08.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 23.45 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 07/24/02 13:01:21 * * 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 2 0 2 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 13 6 7 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,x3,objvar; Integer Variables i1,i2; Equations e1,e2,e3,e4; e1.. sqrt(x3) + i1 + 2*i2 =G= 10; e2.. 0.240038406144983*sqr(i1) - i2 + 0.255036980362153*x3 =G= -3; e3.. sqr(i2) - 1/(POWER(x3,3)*sqrt(x3)) - 4*i1 =G= -12; e4.. - (sqr(i1 - 3) + sqr(i2 - 2) + sqr(4 + x3)) + objvar =E= 0; * set non default bounds i1.up = 200; i2.up = 200; x3.lo = 0.001; x3.up = 200; \$if set nostart \$goto modeldef * set non default levels i1.l = 1; i2.l = 1; x3.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;