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## ex6_2_6.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.
• McDonald, C M, and Floudas, C A, Global Optimization for the Phase Stability Problem. AIChE J. 41 (1995), 1798.
• Original source: Global Model of Chapter 6 ex6.2.6.gms from Floudas e.a. Test Problems

Point:

* NLP written by GAMS Convert at 07/19/01 13:39:46 * * Equation counts * Total E G L N X * 2 2 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 4 4 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 7 4 3 0 * * Solve m using NLP minimizing objvar; Variables objvar,x2,x3,x4; Equations e1,e2; e1.. - ((26.9071667605344*x2 + 41.7710875549227*x3 + 6.30931398488382*x4)*log( 3.9235*x2 + 6.0909*x3 + 0.92*x4) + 0.668686155614739*x2 - 1.14374230885457 *x3 + 2.8906196099828*x4 + 9.58716676053442*x2*log(x2) + 16.9310875549227* x3*log(x3) + 0.309313984883821*x4*log(x4) - 9.58716676053442*x2*log(3.9235 *x2 + 6.0909*x3 + 0.92*x4) - 16.9310875549227*x3*log(3.9235*x2 + 6.0909*x3 + 0.92*x4) - 0.309313984883821*x4*log(3.9235*x2 + 6.0909*x3 + 0.92*x4) + 18.32*x2*log(x2) + 25.84*x3*log(x3) + 7*x4*log(x4) - 18.32*x2*log(3.664*x2 + 5.168*x3 + 1.4*x4) - 25.84*x3*log(3.664*x2 + 5.168*x3 + 1.4*x4) - 7*x4* log(3.664*x2 + 5.168*x3 + 1.4*x4) + (4.0643*x2 + 5.7409*x3 + 1.6741*x4)* log(4.0643*x2 + 5.7409*x3 + 1.6741*x4) + 4.0643*x2*log(x2) + 5.7409*x3* log(x3) + 1.6741*x4*log(x4) - 4.0643*x2*log(4.0643*x2 + 3.22644664511275* x3 + 1.44980651607875*x4) - 5.7409*x3*log(5.31147575751424*x2 + 5.7409*x3 + 0.00729924451284409*x4) - 1.6741*x4*log(2.25846661774355*x2 + 3.70876916588753*x3 + 1.6741*x4) - 30.9714667605344*x2*log(x2) - 47.5119875549227*x3*log(x3) - 7.98341398488382*x4*log(x4)) + objvar =E= 0; e2.. x2 + x3 + x4 =E= 1; * set non default bounds x2.lo = 1E-6; x2.up = 1; x3.lo = 1E-6; x3.up = 1; x4.lo = 1E-6; x4.up = 1; * set non default levels x2.l = 0.51802; x3.l = 0.0511; x4.l = 0.43088; * 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;