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## st_ph14.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 11:34:31 * * Equation counts * Total E G L N X C * 11 1 0 10 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 4 4 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 28 25 3 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,objvar; Positive Variables x1,x2,x3; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11; e1.. x1 =L= 4; e2.. x2 =L= 4; e3.. x3 =L= 4; e4.. 2*x1 + 3*x2 + 4*x3 =L= 35; e5.. 2*x1 + 3*x2 - 4*x3 =L= 19; e6.. 2*x1 - 3*x2 + 4*x3 =L= 23; e7.. - 2*x1 + 3*x2 + 4*x3 =L= 27; e8.. 2*x1 - 3*x2 - 4*x3 =L= 7; e9.. - 2*x1 - 3*x2 + 4*x3 =L= 15; e10.. - 2*x1 + 3*x2 - 4*x3 =L= 11; e11.. - (-3.5*sqr(x1) - 35*x1 - 0.5*sqr(x2) - 3*x2 - 2*sqr(x3) + 4*x3) + 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;