MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex6_2_14

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.69535793 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.69535852 (ANTIGONE) -0.69535830 (BARON) -0.69535793 (COUENNE) -0.69535799 (LINDO) -0.69535963 (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, Global Optimization and Analysis for the Gibbs Free Energy Function Using the UNIFAC, Wilson and ASOG Equations, Industrial and Engineering Chemistry Research, 34:5, 1995, 1674-1687.
Sourceⓘ	Test Problem ex6.2.14 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ⓘ	indefinite
#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ⓘ	9.5173e-02
Maximal coefficientⓘ	3.6838e+00
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(x2/(x2 + x4)) + log(x2/(x2 + 0.095173*x4)))*x2 + (log(x4/(x2 + x4))
      + log(x4/(0.30384*x2 + x4)))*x4 + log(x2 + 2.6738*x4)*(x2 + 2.6738*x4) + 
     log(0.374*x2 + x4)*(0.374*x2 + x4) + 2.6738*log(x4/(x2 + 2.6738*x4))*x4 + 
     0.374*log(x2/(0.374*x2 + x4))*x2 + (log(x3/(x3 + x5)) + log(x3/(x3 + 
     0.095173*x5)))*x3 + (log(x5/(x3 + x5)) + log(x5/(0.30384*x3 + x5)))*x5 + 
     log(x3 + 2.6738*x5)*(x3 + 2.6738*x5) + log(0.374*x3 + x5)*(0.374*x3 + x5)
      + 2.6738*log(x5/(x3 + 2.6738*x5))*x5 + 0.374*log(x3/(0.374*x3 + x5))*x3
      - 3.6838*log(x2)*x2 - 1.59549*log(x4)*x4 - 3.6838*log(x3)*x3 - 1.59549*
     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 = 0.0583;
x3.l = 0.4417;
x4.l = 0.408;
x5.l = 0.092;

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;