MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex6_1_2

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.03246375 p1 ( gdx sol ) (infeas: 9e-19)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.03246663 (ANTIGONE) -0.03246375 (BARON) -0.03246753 (COUENNE) -0.03246375 (LINDO) -0.03246453 (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 for the Phase Stability Problem, AIChE Journal, 41:7, 1995, 1798-1814.
Sourceⓘ	Test Problem ex6.1.2 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ⓘ	3
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	log mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	8
#Nonlinear Nonzeros in Jacobianⓘ	6
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	4
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	4.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.8750e-02
Maximal coefficientⓘ	1.0000e+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
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         13        3       10        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5;

Positive Variables  x4,x5;

Equations  e1,e2,e3,e4;


e1.. -((0.06391 + log(x2))*x2 + (-0.02875 + log(x3))*x3 + 0.925356626778358*x2*
     x5 + 0.746014540096753*x3*x4) + objvar =E= 0;

e2.. x4*(x2 + 0.159040857374844*x3) - x2 =E= 0;

e3.. x5*(0.307941026821595*x2 + x3) - x3 =E= 0;

e4..    x2 + x3 =E= 1;

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

* set non-default levels
x2.l = 0.00421;
x3.l = 0.99579;
x4.l = 0.0258947377097763;
x5.l = 0.998699779997328;

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;