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## ex3_1_3.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.
• Hesse, R, A Heuristic Search Procedure for Estimating a Global Solution of Nonconvex Programming Problems. Op. Res. 21 (1973), 1267.
• Original source: Global Model of Chapter 3 ex3.1.3.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value -310.0000

* NLP written by GAMS Convert at 07/19/01 13:39:32 * * Equation counts * Total E G L N X * 7 1 3 3 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 7 7 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 19 11 8 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,objvar; Positive Variables x1,x2,x4,x6; Equations e1,e2,e3,e4,e5,e6,e7; e1.. - (-25*sqr(x1 - 2) - sqr(x2 - 2) - sqr(x3 - 1) - sqr(x4 - 4) - sqr(x5 - 1 ) - sqr(x6 - 4)) + objvar =E= 0; e2.. sqr(x3 - 3) + x4 =G= 4; e3.. sqr(x5 - 3) + x6 =G= 4; e4.. x1 - 3*x2 =L= 2; e5.. - x1 + x2 =L= 2; e6.. x1 + x2 =L= 6; e7.. x1 + x2 =G= 2; * set non default bounds x3.lo = 1; x3.up = 5; x4.up = 6; x5.lo = 1; x5.up = 5; x6.up = 10; * set non default levels x1.l = 5; x2.l = 1; x3.l = 5; x5.l = 5; x6.l = 10; * 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;