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## ex9_2_2.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.
• Shimizu, K, and Aiyoshi, E, A New Computational Method for Stackelberg and Mim-Max Problems by Use of a Penalty Method. IEEE Trans. on Aut. Control 26 (1981).
• Original source: Global Model of Chapter 9 ex9.2.2.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value 99.9999

* NLP written by GAMS Convert at 07/19/01 13:40:20 * * Equation counts * Total E G L N X * 12 9 0 3 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 * 27 17 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,e11,e12; e1.. x2*x2 + (x3 - 10)*(x3 - 10) - objvar =E= 0; e2.. x2 =L= 15; e3.. - x2 + x3 =L= 0; e4.. - x2 =L= 0; e5.. x2 + x3 + x4 =E= 20; e6.. - x3 + x5 =E= 0; e7.. x3 + x6 =E= 20; e8.. x4*x8 =E= 0; e9.. x5*x9 =E= 0; e10.. x6*x10 =E= 0; e11.. x7*x11 =E= 0; e12.. 2*x2 + 4*x3 + x8 - x9 + x10 =E= 60; * 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;