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## st_ph20.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 11:39:11 * * Equation counts * Total E G L N X C * 10 1 0 9 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 26 2 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; e1.. - 4*x1 - 3*x2 + 4*x3 =L= 30; e2.. 4*x1 + 9*x2 - 2*x3 =L= 114; e3.. 2*x2 - x3 =L= 8; e4.. 2*x1 + 15*x2 - 8*x3 =L= 64; e5.. x2 =L= 14; e6.. - 4*x1 + 3*x2 - 2*x3 =L= -18; e7.. 4*x1 - 9*x2 + 4*x3 =L= -6; e8.. - 6*x1 + 5*x2 - 4*x3 =L= -40; e9.. 4*x1 - 9*x2 - 3*x3 =L= -132; e10.. - (15*x1 - sqr(x1) - sqr(x2) - 2*x2) - 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;