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Instance ex6_2_13

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.21620944 p1 ( gdx sol ) (infeas: 6e-17)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.22496155 (ANTIGONE) -0.21623124 (BARON) -0.28177888 (COUENNE) -0.21687624 (LINDO) -0.27883568 (SCIP) -220.84725550 (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. 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 ex6.2.13 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ⓘ	nonconcave
#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ⓘ	4.8035e-01
Maximal coefficientⓘ	6.0000e+00
Infeasibility of initial pointⓘ	1.11e-16
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(x2/(3*x2 + 6*x4 + x6))*x2 + log(x4/(3*x2 + 6*x4 + x6))*x4 + log(x6/(
     3*x2 + 6*x4 + x6))*x6 - 0.80323071133189*x2 + 1.79175946922805*x4 + 
     0.752006*x6 + log(3*x2 + 6*x4 + 1.6*x6)*(3*x2 + 6*x4 + 1.6*x6) + 2*log(x2/
     (2.00000019368913*x2 + 4.64593*x4 + 0.480353*x6))*x2 + log(x2/(
     1.00772874182154*x2 + 0.724703350369523*x4 + 0.947722362492017*x6))*x2 + 6
     *log(x4/(3.36359157977228*x2 + 6*x4 + 1.13841069150863*x6))*x4 + 1.6*log(
     x6/(1.6359356134845*x2 + 3.39220996773471*x4 + 1.6*x6))*x6 + log(x3/(3*x3
      + 6*x5 + x7))*x3 + log(x5/(3*x3 + 6*x5 + x7))*x5 + log(x7/(3*x3 + 6*x5 + 
     x7))*x7 - 0.80323071133189*x3 + 1.79175946922805*x5 + 0.752006*x7 + log(3*
     x3 + 6*x5 + 1.6*x7)*(3*x3 + 6*x5 + 1.6*x7) + 2*log(x3/(2.00000019368913*x3
      + 4.64593*x5 + 0.480353*x7))*x3 + log(x3/(1.00772874182154*x3 + 
     0.724703350369523*x5 + 0.947722362492017*x7))*x3 + 6*log(x5/(
     3.36359157977228*x3 + 6*x5 + 1.13841069150863*x7))*x5 + 1.6*log(x7/(
     1.6359356134845*x3 + 3.39220996773471*x5 + 1.6*x7))*x7 - 3*log(x2)*x2 - 6*
     log(x4)*x4 - 1.6*log(x6)*x6 - 3*log(x3)*x3 - 6*log(x5)*x5 - 1.6*log(x7)*x7
     ) + objvar =E= 0;

e2..    x2 + x3 =E= 0.08;

e3..    x4 + x5 =E= 0.3;

e4..    x6 + x7 =E= 0.62;

* set non-default bounds
x2.lo = 1E-7; x2.up = 0.08;
x3.lo = 1E-7; x3.up = 0.08;
x4.lo = 1E-7; x4.up = 0.3;
x5.lo = 1E-7; x5.up = 0.3;
x6.lo = 1E-7; x6.up = 0.62;
x7.lo = 1E-7; x7.up = 0.62;

* set non-default levels
x2.l = 0.0739;
x3.l = 0.0061;
x4.l = 0.2773;
x5.l = 0.0227;
x6.l = 0.5731;
x7.l = 0.0469;

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;