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## ex8_6_2.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 8 ex8.6.2.gms from Floudas e.a. Test Problems

Point:

* NLP written by GAMS Convert at 07/19/01 13:40:16 * * Equation counts * Total E G L N X * 1 1 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 31 31 0 0 0 0 0 0 * FX 6 6 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 31 1 30 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,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,objvar; Positive Variables x1,x11,x12,x21,x22,x23; Equations e1; e1.. - (sqr(1 - exp(3 - 3*(sqr(x1 - x2) + sqr(x11 - x12) + sqr(x21 - x22))** 0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x3) + sqr(x11 - x13) + sqr(x21 - x23)) **0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x4) + sqr(x11 - x14) + sqr(x21 - x24 ))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x5) + sqr(x11 - x15) + sqr(x21 - x25))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x6) + sqr(x11 - x16) + sqr(x21 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x7) + sqr(x11 - x17) + sqr( x21 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x8) + sqr(x11 - x18) + sqr(x21 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x9) + sqr(x11 - x19) + sqr(x21 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x10) + sqr(x11 - x20) + sqr(x21 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x3) + sqr(x12 - x13) + sqr(x22 - x23))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x4) + sqr( x12 - x14) + sqr(x22 - x24))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x5) + sqr(x12 - x15) + sqr(x22 - x25))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x6) + sqr(x12 - x16) + sqr(x22 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x7) + sqr(x12 - x17) + sqr(x22 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x8) + sqr(x12 - x18) + sqr(x22 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr( x2 - x9) + sqr(x12 - x19) + sqr(x22 - x29))**0.5)) + sqr(1 - exp(3 - 3*( sqr(x2 - x10) + sqr(x12 - x20) + sqr(x22 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x3 - x4) + sqr(x13 - x14) + sqr(x23 - x24))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x3 - x5) + sqr(x13 - x15) + sqr(x23 - x25))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x3 - x6) + sqr(x13 - x16) + sqr(x23 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x3 - x7) + sqr(x13 - x17) + sqr(x23 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x3 - x8) + sqr(x13 - x18) + sqr(x23 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x3 - x9) + sqr(x13 - x19) + sqr(x23 - x29))**0.5 )) + sqr(1 - exp(3 - 3*(sqr(x3 - x10) + sqr(x13 - x20) + sqr(x23 - x30))** 0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x5) + sqr(x14 - x15) + sqr(x24 - x25)) **0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x6) + sqr(x14 - x16) + sqr(x24 - x26 ))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x7) + sqr(x14 - x17) + sqr(x24 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x8) + sqr(x14 - x18) + sqr(x24 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x9) + sqr(x14 - x19) + sqr( x24 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x10) + sqr(x14 - x20) + sqr(x24 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x6) + sqr(x15 - x16) + sqr(x25 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x7) + sqr(x15 - x17) + sqr(x25 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x8) + sqr(x15 - x18) + sqr(x25 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x9) + sqr( x15 - x19) + sqr(x25 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x10) + sqr(x15 - x20) + sqr(x25 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 - x7) + sqr(x16 - x17) + sqr(x26 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 - x8) + sqr(x16 - x18) + sqr(x26 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 - x9) + sqr(x16 - x19) + sqr(x26 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr( x6 - x10) + sqr(x16 - x20) + sqr(x26 - x30))**0.5)) + sqr(1 - exp(3 - 3*( sqr(x7 - x8) + sqr(x17 - x18) + sqr(x27 - x28))**0.5)) + sqr(1 - exp(3 - 3 *(sqr(x7 - x9) + sqr(x17 - x19) + sqr(x27 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x7 - x10) + sqr(x17 - x20) + sqr(x27 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x8 - x9) + sqr(x18 - x19) + sqr(x28 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x8 - x10) + sqr(x18 - x20) + sqr(x28 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x9 - x10) + sqr(x19 - x20) + sqr(x29 - x30))**0.5)) ) + objvar =E= -45; * set non default bounds x1.fx = 0; x2.lo = -5; x2.up = 5; x3.lo = -5; x3.up = 5; x4.lo = -5; x4.up = 5; x5.lo = -5; x5.up = 5; x6.lo = -5; x6.up = 5; x7.lo = -5; x7.up = 5; x8.lo = -5; x8.up = 5; x9.lo = -5; x9.up = 5; x10.lo = -5; x10.up = 5; x11.fx = 0; x12.fx = 0; x13.lo = -5; x13.up = 5; x14.lo = -5; x14.up = 5; x15.lo = -5; x15.up = 5; x16.lo = -5; x16.up = 5; x17.lo = -5; x17.up = 5; x18.lo = -5; x18.up = 5; x19.lo = -5; x19.up = 5; x20.lo = -5; x20.up = 5; x21.fx = 0; x22.fx = 0; x23.fx = 0; x24.lo = -5; x24.up = 5; x25.lo = -5; x25.up = 5; x26.lo = -5; x26.up = 5; x27.lo = -5; x27.up = 5; x28.lo = -5; x28.up = 5; x29.lo = -5; x29.up = 5; x30.lo = -5; x30.up = 5; * set non default levels x2.l = 3.43266708; x3.l = 0.50375356; x4.l = -1.98862096; x5.l = -2.07787883; x6.l = -2.75947133; x7.l = -1.50169496; x8.l = 3.56270347; x9.l = -4.32886277; x10.l = 0.00210668999999974; x13.l = 4.91133039; x14.l = 2.62250467; x15.l = -3.69307517; x16.l = 1.39718759; x17.l = -3.40482136; x18.l = -2.49919467; x19.l = 1.68928609; x20.l = -0.64643619; x24.l = -3.49898212; x25.l = 0.8911365; x26.l = 3.30892812; x27.l = -2.69184262; x28.l = 1.6573446; x29.l = 2.75857606; x30.l = -1.96341523; * 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;