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## ex6_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.
• McDonald, C M, and Floudas, C A, Global Optimization for the Phase and Chemical Equilibrium Problem: Application to the NRTL Equation. Comput. Chem. Eng. 19 (1995), 1.
• Castillo, J, and Grossmann, I E, Computation of Phase and Chemical Equilibria. Comput. Chem. Eng. 5 (1981), 99.
• Original source: Global Model of Chapter 6 ex6.1.3.gms from Floudas e.a. Test Problems

Point:

* NLP written by GAMS Convert at 07/19/01 13:39:42 * * Equation counts * Total E G L N X * 10 10 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 13 13 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 43 7 36 0 * * Solve m using NLP minimizing objvar; Variables objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13; Positive Variables x8,x9,x10,x11,x12,x13; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10; e1.. - (x2*(log(x2) - log(x2 + x4 + x6)) + x4*(log(x4) - log(x2 + x4 + x6)) + x6*(log(x6) - log(x2 + x4 + x6)) + x3*(log(x3) - log(x3 + x5 + x7)) + x5*( log(x5) - log(x3 + x5 + x7)) + x7*(log(x7) - log(x3 + x5 + x7)) + x2*( 1.44805026165593*x10 + 0.989428667054834*x12) + x4*(1.12676386427658*x8 + 1.00363012835441*x12) + x6*(0.0347225450624344*x8 + 0.82681418300153*x10) + x3*(1.44805026165593*x11 + 0.989428667054834*x13) + x5*( 1.12676386427658*x9 + 1.00363012835441*x13) + x7*(0.0347225450624344*x9 + 0.82681418300153*x11)) + objvar =E= 0; e2.. x8*(x2 + 0.145002897355373*x4 + 0.989528214945409*x6) - x2 =E= 0; e3.. x9*(x3 + 0.145002897355373*x5 + 0.989528214945409*x7) - x3 =E= 0; e4.. x10*(0.293701311601799*x2 + x4 + 0.646291923054068*x6) - x4 =E= 0; e5.. x11*(0.293701311601799*x3 + x5 + 0.646291923054068*x7) - x5 =E= 0; e6.. x12*(0.619143628558899*x2 + 0.239837817616513*x4 + x6) - x6 =E= 0; e7.. x13*(0.619143628558899*x3 + 0.239837817616513*x5 + x7) - x7 =E= 0; e8.. x2 + x3 =E= 0.2995; e9.. x4 + x5 =E= 0.1998; e10.. x6 + x7 =E= 0.4994; * set non default bounds x2.lo = 1E-7; x2.up = 0.2995; x3.lo = 1E-7; x3.up = 0.2995; x4.lo = 1E-7; x4.up = 0.1998; x5.lo = 1E-7; x5.up = 0.1998; x6.lo = 1E-7; x6.up = 0.4994; x7.lo = 1E-7; x7.up = 0.4994; * set non default levels x2.l = 0.29949; x3.l = 1E-5; x4.l = 0.06551; x5.l = 0.13429; x6.l = 0.49873; x7.l = 0.00067; x8.l = 0.373197867737302; x9.l = 0.000496390669236887; x10.l = 0.137685122950498; x11.l = 0.996764152762375; x12.l = 0.71260468488485; x13.l = 0.0203746428730577; * 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;