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## ex9_1_5.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.
• Bard, J F, Some Properties of the Bilevel Programming Problem. Journal of Optimization Theory and Applications 68 (1991), 371-378.
• Original source: Global Model of Chapter 9 ex9.1.5.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value -1.0000

* NLP written by GAMS Convert at 07/19/01 13:40:18 * * Equation counts * Total E G L N X * 13 13 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 14 14 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 33 23 10 0 * * Solve m using NLP minimizing objvar; Variables objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14; Positive Variables x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13; e1.. - objvar - x2 + 10*x3 - x4 =E= 0; e2.. x2 + x3 + x5 =E= 1; e3.. x2 + x4 + x6 =E= 1; e4.. x3 + x4 + x7 =E= 1; e5.. - x3 + x8 =E= 0; e6.. - x4 + x9 =E= 0; e7.. x10*x5 =E= 0; e8.. x11*x6 =E= 0; e9.. x12*x7 =E= 0; e10.. x13*x8 =E= 0; e11.. x14*x9 =E= 0; e12.. x10 + x12 - x13 =E= 1; e13.. x11 + x12 - x14 =E= 1; * 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;