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## ex5_2_4.gms:

#### References:

• Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
• Ben-Tal, A, Eiger, G, and Gershovitz, V, Global Minimization by Reducing the Duality Gap. Mathematical Programming 63 (1994), 193-212.
• Original source: Global Model of Chapter 5 ex5.2.4.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value -450.0000

* NLP written by GAMS Convert at 07/19/01 13:39:38 * * Equation counts * Total E G L N X * 7 2 0 5 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 8 8 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 28 12 16 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,objvar; Positive Variables x1,x2,x3,x4,x5,x6,x7; Equations e1,e2,e3,e4,e5,e6,e7; e1.. - ((9 + (-6*x1) - 16*x2 - 15*x3)*x4 + (15 + (-6*x1) - 16*x2 - 15*x3)*x5) + x6 - 5*x7 - objvar =E= 0; e2.. x3*x4 + x3*x5 =L= 50; e3.. x4 + x6 =L= 100; e4.. x5 + x7 =L= 200; e5.. (3*x1 + x2 + x3 - 2.5)*x4 - 0.5*x6 =L= 0; e6.. (3*x1 + x2 + x3 - 1.5)*x5 + 0.5*x7 =L= 0; e7.. x1 + x2 + x3 =E= 1; * set non default bounds x1.up = 1; x2.up = 1; x3.up = 1; x4.up = 100; x5.up = 200; x6.up = 100; x7.up = 200; * 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;