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Instance ex6_2_10

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-3.05197613 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-3.05198213 (ANTIGONE) -3.05197613 (BARON) -3.65267227 (COUENNE) -3.05198155 (GUROBI) -3.05202448 (LINDO) -4.20104013 (SCIP) -1090.27489100 (SHOT)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford 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, GLOPEQ: A New Computational Tool for the Phase and Chemical Equilibrium Problem, Computers and Chemical Engineering, 21:1, 1997, 1-23. Magnussen, T, Rasmussen, P, and Fredenslund, A, UNIFAC Parameter Table for Prediction of Liquid-Liquid Equilibria, Industrial and Engineering Chemistry Process Design and Development, 20:2, 1981, 331-339.
Sourceⓘ	Test Problem ex6.2.10 of Chapter 6 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	6
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	3
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div log mul
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	6
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	18
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	6
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.1562e-01
Maximal coefficientⓘ	2.5604e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        4        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         13        7        6        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7;

Equations  e1,e2,e3,e4;


e1.. -(log(2.1055*x2 + 3.1878*x4 + 0.92*x6)*(15.3261663216011*x2 + 
     23.2043471859416*x4 + 6.69678129464404*x6) - 2.46348749603266*x2 - 
     4.33155441248417*x4 - 0.626542690017204*x6 + 6.4661663216011*log(x2/(
     2.1055*x2 + 3.1878*x4 + 0.92*x6))*x2 + 12.2043471859416*log(x4/(2.1055*x2
      + 3.1878*x4 + 0.92*x6))*x4 + 0.696781294644034*log(x6/(2.1055*x2 + 3.1878
     *x4 + 0.92*x6))*x6 + 9.86*log(x2/(1.972*x2 + 2.4*x4 + 1.4*x6))*x2 + 12*
     log(x4/(1.972*x2 + 2.4*x4 + 1.4*x6))*x4 + 7*log(x6/(1.972*x2 + 2.4*x4 + 
     1.4*x6))*x6 + log(1.972*x2 + 2.4*x4 + 1.4*x6)*(1.972*x2 + 2.4*x4 + 1.4*x6)
      + 1.972*log(x2/(1.972*x2 + 0.283910843616504*x4 + 3.02002220174195*x6))*
     x2 + 2.4*log(x4/(1.45991339466884*x2 + 2.4*x4 + 0.415073537580851*x6))*x4
      + 1.4*log(x6/(0.602183324335333*x2 + 0.115623371371275*x4 + 1.4*x6))*x6
      + log(2.1055*x3 + 3.1878*x5 + 0.92*x7)*(15.3261663216011*x3 + 
     23.2043471859416*x5 + 6.69678129464404*x7) - 2.46348749603266*x3 - 
     4.33155441248417*x5 - 0.626542690017204*x7 + 6.4661663216011*log(x3/(
     2.1055*x3 + 3.1878*x5 + 0.92*x7))*x3 + 12.2043471859416*log(x5/(2.1055*x3
      + 3.1878*x5 + 0.92*x7))*x5 + 0.696781294644034*log(x7/(2.1055*x3 + 3.1878
     *x5 + 0.92*x7))*x7 + 9.86*log(x3/(1.972*x3 + 2.4*x5 + 1.4*x7))*x3 + 12*
     log(x5/(1.972*x3 + 2.4*x5 + 1.4*x7))*x5 + 7*log(x7/(1.972*x3 + 2.4*x5 + 
     1.4*x7))*x7 + log(1.972*x3 + 2.4*x5 + 1.4*x7)*(1.972*x3 + 2.4*x5 + 1.4*x7)
      + 1.972*log(x3/(1.972*x3 + 0.283910843616504*x5 + 3.02002220174195*x7))*
     x3 + 2.4*log(x5/(1.45991339466884*x3 + 2.4*x5 + 0.415073537580851*x7))*x5
      + 1.4*log(x7/(0.602183324335333*x3 + 0.115623371371275*x5 + 1.4*x7))*x7
      - 17.2981663216011*log(x2)*x2 - 25.6043471859416*log(x4)*x4 - 
     8.09678129464404*log(x6)*x6 - 17.2981663216011*log(x3)*x3 - 
     25.6043471859416*log(x5)*x5 - 8.09678129464404*log(x7)*x7) + objvar =E= 0;

e2..    x2 + x3 =E= 0.2;

e3..    x4 + x5 =E= 0.4;

e4..    x6 + x7 =E= 0.4;

* set non-default bounds
x2.lo = 1E-7; x2.up = 0.2;
x3.lo = 1E-7; x3.up = 0.2;
x4.lo = 1E-7; x4.up = 0.4;
x5.lo = 1E-7; x5.up = 0.4;
x6.lo = 1E-7; x6.up = 0.4;
x7.lo = 1E-7; x7.up = 0.4;

* set non-default levels
x2.l = 0.19863;
x3.l = 0.00137;
x4.l = 0.00428;
x5.l = 0.39572;
x6.l = 0.39922;
x7.l = 0.00078;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;