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## st_ph1.gms:

#### References:

• Tawarmalani, M, and Sahinidis, N, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, 2002.
• Shectman, J P, and Sahinidis, N, A finite algorithm for global minimization of separable concave programs. Journal of Global Optimization 12 (1998), 1--36.
• Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, 1999. PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne

Point:

* NLP written by GAMS Convert at 08/30/02 11:37:50 * * Equation counts * Total E G L N X C * 6 1 0 5 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 7 7 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 31 25 6 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,objvar; Positive Variables x1,x2,x3,x4,x5,x6; Equations e1,e2,e3,e4,e5,e6; e1.. 6*x1 + x2 + 9*x4 + 3*x5 + 5*x6 =L= 96; e2.. x1 + 7*x3 + 6*x4 + 2*x5 + 2*x6 =L= 72; e3.. 5*x1 + 4*x2 + x3 + 3*x4 + 8*x5 =L= 84; e4.. 9*x1 + x2 + 2*x4 + 7*x5 + 6*x6 =L= 100; e5.. 2*x1 + 6*x4 + 3*x5 + 9*x6 =L= 80; e6.. - (x1 - 0.5*sqr(x1) - 0.5*sqr(x2) + x2 - 0.5*sqr(x3) + x3 - 0.5*sqr(x4) + x4 - 0.5*sqr(x5) + x5 - 0.5*sqr(x6) + x6) + objvar =E= 0; * set non default bounds * set non default levels * set non default marginals Model m / all /; m.limrow=0; m.limcol=0; \$if NOT '%gams.u1%' == '' \$include '%gams.u1%' Solve m using NLP minimizing objvar;