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## ex9_2_7.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.
• Visweswaran, V, A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs. In Floudas, C A, and Pardalos, P M, Eds, State of the Art in Global Optimization. Kluwer Academic Publishers, 1996, p. 139.
• Original source: Global Model of Chapter 9 ex9.2.7.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value 17.0000

* NLP written by GAMS Convert at 07/19/01 13:40:22 * * Equation counts * Total E G L N X * 10 10 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 11 11 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 28 18 10 0 * * Solve m using NLP minimizing objvar; Variables objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11; Positive Variables x2,x3,x4,x5,x6,x7,x8,x9,x10,x11; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10; e1.. (x2 - 5)*(x2 - 5) + (1 + 2*x3)*(1 + 2*x3) - objvar =E= 0; e2.. - 3*x2 + x3 + x4 =E= -3; e3.. x2 - 0.5*x3 + x5 =E= 4; e4.. x2 + x3 + x6 =E= 7; e5.. - x3 + x7 =E= 0; e6.. x4*x8 =E= 0; e7.. x5*x9 =E= 0; e8.. x6*x10 =E= 0; e9.. x7*x11 =E= 0; e10.. - 1.5*x2 + 2*x3 + x8 - 0.5*x9 + x10 - x11 =E= 2; * set non default bounds x4.up = 20; x5.up = 20; x6.up = 20; x7.up = 20; x8.up = 20; x9.up = 20; x10.up = 20; x11.up = 20; * 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;