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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex6_2_12

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.28919475 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.28919407 (ANTIGONE) 0.28919357 (BARON) 0.28906627 (COUENNE) 0.28919052 (LINDO) 0.28916337 (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.
Sourceⓘ	Test Problem ex6.2.12 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ⓘ	6.9623e-02
Maximal coefficientⓘ	8.9606e+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/(8*x2 + x4))*x2 + log(x4/(8*x2 + x4))*x4 + 0.0696225416798359*x2
      + 0.752006*x4 + log(8*x2 + 1.6*x4)*(8*x2 + 1.6*x4) + 5*log(x2/(
     5.00000397494442*x2 + 0.480353357956269*x4))*x2 + 3*log(x2/(
     8.96062592375197*x2 + 1.13841069150863*x4))*x2 + 1.6*log(x4/(
     1.69889877049372*x2 + 1.6*x4))*x4 + log(x3/(8*x3 + x5))*x3 + log(x5/(8*x3
      + x5))*x5 + 0.0696225416798359*x3 + 0.752006*x5 + log(8*x3 + 1.6*x5)*(8*
     x3 + 1.6*x5) + 5*log(x3/(5.00000397494442*x3 + 0.480353357956269*x5))*x3
      + 3*log(x3/(8.96062592375197*x3 + 1.13841069150863*x5))*x3 + 1.6*log(x5/(
     1.69889877049372*x3 + 1.6*x5))*x5 - 8*log(x2)*x2 - 1.6*log(x4)*x4 - 8*log(
     x3)*x3 - 1.6*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 = 0.4994;
x3.l = 0.0006;
x4.l = 0.1179;
x5.l = 0.3821;

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;