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## ex9_1_8.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, and Falk, J E, An Explicit Solution to the Multi-Level Programming Problem. Comp. Op. Res. 9 (1982), 77-100.
• Original source: Global Model of Chapter 9 ex9.1.8.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value -3.2500

* NLP written by GAMS Convert at 07/19/01 13:40:19 * * Equation counts * Total E G L N X * 13 12 0 1 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 15 15 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,x15; Positive Variables x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13; e1.. - objvar - 2*x2 + x3 + 0.5*x4 =E= 0; e2.. x2 + x3 =L= 2; e3.. - 2*x2 + x4 - x5 + x6 =E= -2.5; e4.. x2 - 3*x3 + x5 + x7 =E= 2; e5.. - x4 + x8 =E= 0; e6.. - x5 + x9 =E= 0; e7.. x11*x6 =E= 0; e8.. x12*x7 =E= 0; e9.. x13*x8 =E= 0; e10.. x14*x9 =E= 0; e11.. x15*x10 =E= 0; e12.. x11 - x13 =E= 4; 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;