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ex8_4_4.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.
• Esposito, W R, and Floudas, C A, Global Optimization in Parameter Estimation of Nonlinear Algebraic Models via the Error-in-Variables Approach. Ind. Eng. Chem. Res. 35 (1998), 1841-1858.
• Csendes, T, and Ratz, D, Subdivision Direction Selection in Interval Methods for Global Optimization. Journal of Global Optimization 7 (1995), 183.
• Original source: Global Model of Chapter 8 ex8.4.4.gms from Floudas e.a. Test Problems

Point: p1
Best known point: p1 with value 0.2125

* NLP written by GAMS Convert at 07/19/01 13:40:11 * * Equation counts * Total E G L N X * 13 13 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 18 18 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 61 25 36 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,objvar; Negative Variables x6; Positive Variables x13,x14,x16,x17; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13; e1.. - (sqr(x1 - 5) + sqr(5 + x2) + sqr(x3 - 3) + sqr(2 + x4) + sqr(x5 - 2) + sqr(1 + x6) + sqr(x7 - 1.5) + sqr(0.5 + x8) + sqr(x9 - 1.2) + sqr(0.2 + x10) + sqr(x11 - 1.1) + sqr(0.1 + x12)) + objvar =E= 0; e2.. x14/0.1570795**x15 - x1 + x13 =E= 0; e3.. x14/0.314159**x15 - x3 + x13 =E= 0; e4.. x14/0.4712385**x15 - x5 + x13 =E= 0; e5.. x14/0.628318**x15 - x7 + x13 =E= 0; e6.. x14/0.7853975**x15 - x9 + x13 =E= 0; e7.. x14/0.942477**x15 - x11 + x13 =E= 0; e8.. - x17/0.1570795**x15 - x2 + 0.1570795*x16 =E= 0; e9.. - x17/0.314159**x15 - x4 + 0.314159*x16 =E= 0; e10.. - x17/0.4712385**x15 - x6 + 0.4712385*x16 =E= 0; e11.. - x17/0.628318**x15 - x8 + 0.628318*x16 =E= 0; e12.. - x17/0.7853975**x15 - x10 + 0.7853975*x16 =E= 0; e13.. - x17/0.942477**x15 - x12 + 0.942477*x16 =E= 0; * set non default bounds x1.lo = 4; x1.up = 6; x2.lo = -6; x2.up = -4; x3.lo = 2; x3.up = 4; x4.lo = -3; x4.up = -1; x5.lo = 1; x5.up = 3; x6.lo = -2; x7.lo = 0.5; x7.up = 2.5; x8.lo = -1.5; x8.up = 0.5; x9.lo = 0.2; x9.up = 2.2; x10.lo = -1.2; x10.up = 0.8; x11.lo = 0.1; x11.up = 2.1; x12.lo = -1.1; x12.up = 0.9; x13.up = 1; x14.up = 1; x15.lo = 1.1; x15.up = 1.3; x16.up = 1; x17.up = 1; * set non default levels x1.l = 4.343494264; x2.l = -4.313466584; x3.l = 3.100750712; x4.l = -2.397724192; x5.l = 1.584424234; x6.l = -1.551894266; x7.l = 1.199661008; x8.l = 0.212540694; x9.l = 0.334227446; x10.l = -0.199578662; x11.l = 2.096235254; x12.l = 0.057466756; x13.l = 0.991133039; x14.l = 0.762250467; x15.l = 1.1261384966; x16.l = 0.639718759; x17.l = 0.159517864; * 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;