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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex6_2_11

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.00000267 p1 ( gdx sol ) (infeas: 2e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000685 (ANTIGONE) -0.00000267 (BARON) -0.00044799 (COUENNE) -0.00000477 (GUROBI) -0.00000267 (LINDO) -0.00010068 (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, Global Optimization for the Phase and Chemical Equilibrium Problem, PhD thesis, Princeton University, 1995.
Sourceⓘ	Test Problem ex6.2.11 of Chapter 6 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	1
#Linear Constraintsⓘ	1
#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ⓘ	3
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	1
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
*          2        2        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        4        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        4        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4;

Equations  e1,e2;


e1.. -(log(2.1055*x2 + 3.1878*x3 + 0.92*x4)*(15.3261663216011*x2 + 
     23.2043471859416*x3 + 6.69678129464404*x4) + 1.04055250396734*x2 - 
     2.24199441248417*x3 + 3.1618173099828*x4 + 6.4661663216011*log(x2/(2.1055*
     x2 + 3.1878*x3 + 0.92*x4))*x2 + 12.2043471859416*log(x3/(2.1055*x2 + 
     3.1878*x3 + 0.92*x4))*x3 + 0.696781294644034*log(x4/(2.1055*x2 + 3.1878*x3
      + 0.92*x4))*x4 + 9.86*log(x2/(1.972*x2 + 2.4*x3 + 1.4*x4))*x2 + 12*log(x3
     /(1.972*x2 + 2.4*x3 + 1.4*x4))*x3 + 7*log(x4/(1.972*x2 + 2.4*x3 + 1.4*x4))
     *x4 + log(1.972*x2 + 2.4*x3 + 1.4*x4)*(1.972*x2 + 2.4*x3 + 1.4*x4) + 1.972
     *log(x2/(1.972*x2 + 0.283910843616504*x3 + 3.02002220174195*x4))*x2 + 2.4*
     log(x3/(1.45991339466884*x2 + 2.4*x3 + 0.415073537580851*x4))*x3 + 1.4*
     log(x4/(0.602183324335333*x2 + 0.115623371371275*x3 + 1.4*x4))*x4 - 
     17.2981663216011*log(x2)*x2 - 25.6043471859416*log(x3)*x3 - 
     8.09678129464404*log(x4)*x4) + objvar =E= 0;

e2..    x2 + x3 + x4 =E= 1;

* set non-default bounds
x2.lo = 1E-6; x2.up = 1;
x3.lo = 1E-6; x3.up = 1;
x4.lo = 1E-6; x4.up = 1;

* set non-default levels
x2.l = 0.00565;
x3.l = 0.99054;
x4.l = 0.00381;

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;