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## ex2_1_7.gms:

#### Reference:

• 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.
• Original source: Global Model of Chapter 2 ex2.1.7.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value -4150.4101

* NLP written by GAMS Convert at 07/19/01 13:39:30 * * Equation counts * Total E G L N X * 11 1 0 10 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 21 21 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 185 165 20 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19 ,x20,objvar; Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17 ,x18,x19,x20; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11; e1.. 0.5*(sqr(x1 - 2) + 2*sqr(x2 - 2) + 3*sqr(x3 - 2) + 4*sqr(x4 - 2) + 5*sqr( x5 - 2) + 6*sqr(x6 - 2) + 7*sqr(x7 - 2) + 8*sqr(x8 - 2) + 9*sqr(x9 - 2) + 10*sqr(x10 - 2) + 11*sqr(x11 - 2) + 12*sqr(x12 - 2) + 13*sqr(x13 - 2) + 14 *sqr(x14 - 2) + 15*sqr(x15 - 2) + 16*sqr(x16 - 2) + 17*sqr(x17 - 2) + 18* sqr(x18 - 2) + 19*sqr(x19 - 2) + 20*sqr(x20 - 2)) + objvar =E= 0; e2.. - 3*x1 + 7*x2 - 5*x4 + x5 + x6 + 2*x8 - x9 - x10 - 9*x11 + 3*x12 + 5*x13 + x16 + 7*x17 - 7*x18 - 4*x19 - 6*x20 =L= -5; e3.. 7*x1 - 5*x3 + x4 + x5 + 2*x7 - x8 - x9 - 9*x10 + 3*x11 + 5*x12 + x15 + 7*x16 - 7*x17 - 4*x18 - 6*x19 - 3*x20 =L= 2; e4.. - 5*x2 + x3 + x4 + 2*x6 - x7 - x8 - 9*x9 + 3*x10 + 5*x11 + x14 + 7*x15 - 7*x16 - 4*x17 - 6*x18 - 3*x19 + 7*x20 =L= -1; e5.. - 5*x1 + x2 + x3 + 2*x5 - x6 - x7 - 9*x8 + 3*x9 + 5*x10 + x13 + 7*x14 - 7*x15 - 4*x16 - 6*x17 - 3*x18 + 7*x19 =L= -3; e6.. x1 + x2 + 2*x4 - x5 - x6 - 9*x7 + 3*x8 + 5*x9 + x12 + 7*x13 - 7*x14 - 4*x15 - 6*x16 - 3*x17 + 7*x18 - 5*x20 =L= 5; e7.. x1 + 2*x3 - x4 - x5 - 9*x6 + 3*x7 + 5*x8 + x11 + 7*x12 - 7*x13 - 4*x14 - 6*x15 - 3*x16 + 7*x17 - 5*x19 + x20 =L= 4; e8.. 2*x2 - x3 - x4 - 9*x5 + 3*x6 + 5*x7 + x10 + 7*x11 - 7*x12 - 4*x13 - 6*x14 - 3*x15 + 7*x16 - 5*x18 + x19 + x20 =L= -1; e9.. 2*x1 - x2 - x3 - 9*x4 + 3*x5 + 5*x6 + x9 + 7*x10 - 7*x11 - 4*x12 - 6*x13 - 3*x14 + 7*x15 - 5*x17 + x18 + x19 =L= 0; e10.. - x1 - x2 - 9*x3 + 3*x4 + 5*x5 + x8 + 7*x9 - 7*x10 - 4*x11 - 6*x12 - 3*x13 + 7*x14 - 5*x16 + x17 + x18 + 2*x20 =L= 9; e11.. x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + x19 + x20 =L= 40; * set non default bounds * set non default levels x3.l = 1.04289; x11.l = 1.74674; x13.l = 0.43147; x16.l = 4.43305; x18.l = 15.85893; x20.l = 16.4889; * 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;