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Instance ex6_2_9

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.03406618 p1 ( gdx sol ) (infeas: 1e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.03406934 (ANTIGONE) -0.03406618 (BARON) -0.03406618 (COUENNE) -0.03407019 (GUROBI) -0.03407258 (LINDO) -0.06403057 (SCIP)
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. Heidemann, R and Mandhane, J, Some Properties of the NRTL Equation in Correlating Liquid-Liquid Equilibrium Data, Chemical Engineering Science, 28:5, 1973, 1213-1221.
Sourceⓘ	Test Problem ex6.2.9 of Chapter 6 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconvex
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	2
#Linear Constraintsⓘ	2
#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ⓘ	4
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	8
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	4.4374e-01
Maximal coefficientⓘ	3.5679e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        3        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          9        5        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5;

Equations  e1,e2,e3;


e1.. -(log(4.8274*x2 + 0.92*x4)*(31.4830434782609*x2 + 6*x4) - 1.36551138119385
     *x2 + 2.8555953099828*x4 + 11.5030434782609*log(x2/(4.8274*x2 + 0.92*x4))*
     x2 + 20.98*log(x2/(4.196*x2 + 1.4*x4))*x2 + 7*log(x4/(4.196*x2 + 1.4*x4))*
     x4 + log(4.196*x2 + 1.4*x4)*(4.196*x2 + 1.4*x4) + 1.62*log(x2/(
     7.52678200680961*x2 + 0.443737968424621*x4))*x2 + 0.848*log(x2/(
     7.52678200680961*x2 + 0.443737968424621*x4))*x2 + 1.728*log(x2/(
     1.82245052351472*x2 + 1.4300083598626*x4))*x2 + 1.4*log(x4/(
     0.504772348000588*x2 + 1.4*x4))*x4 + log(4.8274*x3 + 0.92*x5)*(
     31.4830434782609*x3 + 6*x5) - 1.36551138119385*x3 + 2.8555953099828*x5 + 
     11.5030434782609*log(x3/(4.8274*x3 + 0.92*x5))*x3 + 20.98*log(x3/(4.196*x3
      + 1.4*x5))*x3 + 7*log(x5/(4.196*x3 + 1.4*x5))*x5 + log(4.196*x3 + 1.4*x5)
     *(4.196*x3 + 1.4*x5) + 1.62*log(x3/(7.52678200680961*x3 + 
     0.443737968424621*x5))*x3 + 0.848*log(x3/(7.52678200680961*x3 + 
     0.443737968424621*x5))*x3 + 1.728*log(x3/(1.82245052351472*x3 + 
     1.4300083598626*x5))*x3 + 1.4*log(x5/(0.504772348000588*x3 + 1.4*x5))*x5
      - 35.6790434782609*log(x2)*x2 - 7.4*log(x4)*x4 - 35.6790434782609*log(x3)
     *x3 - 7.4*log(x5)*x5) + objvar =E= 0;

e2..    x2 + x3 =E= 0.5;

e3..    x4 + x5 =E= 0.5;

* set non-default bounds
x2.lo = 1E-7; x2.up = 0.5;
x3.lo = 1E-7; x3.up = 0.5;
x4.lo = 1E-7; x4.up = 0.5;
x5.lo = 1E-7; x5.up = 0.5;

* set non-default levels
x2.l = 0.4998;
x3.l = 0.0002;
x4.l = 0.0451;
x5.l = 0.4549;

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;