MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance ex8_5_6

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000099 p1 ( gdx sol ) (infeas: 2e-14) -0.00116737 p2 ( gdx sol ) (infeas: 2e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00122726 (COUENNE) -0.00116848 (LINDO) -0.00117041 (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. Hua, J, Brennecke, J, and Stadtherr, M, Enhanced Interval Analysis for Phase Stability: Cubic Equation of State Models, Industrial and Engineering Chemistry Research, 37:4, 1998, 1519-1527.
Sourceⓘ	Test Problem ex8.5.6 of Chapter 8 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ⓘ	unknown
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	4
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div log mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	14
#Nonlinear Nonzeros in Jacobianⓘ	6
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	17
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	5
#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ⓘ	8.1525e-02
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          5        5        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
*         21        9       12        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7;

Equations  e1,e2,e3,e4,e5;


e1.. -(log(x2)*x2 + log(x3)*x3 + log(x4)*x4 - log(x5 - x7) + x5 - 
     0.353553390593274*log((x5 + 2.41421356237309*x7)/(x5 - 0.414213562373095*
     x7))*x6/x7 + 1.42876598488588*x2 + 1.27098480432594*x3 + 1.62663700075562*
     x4) + objvar =E= -1;

e2.. POWER(x5,3) - sqr(x5)*(1 - x7) + (-3*sqr(x7) - 2*x7 + x6)*x5 - x6*x7 + 
     POWER(x7,3) + sqr(x7) =E= 0;

e3.. -(0.142724*x2*x2 + 0.206577*x2*x3 + 0.342119*x2*x4 + 0.206577*x3*x2 + 
     0.323084*x3*x3 + 0.547748*x3*x4 + 0.342119*x4*x2 + 0.547748*x4*x3 + 
     0.968906*x4*x4) + x6 =E= 0;

e4..  - 0.0815247*x2 - 0.0907391*x3 - 0.13705*x4 + x7 =E= 0;

e5..    x2 + x3 + x4 =E= 1;

* set non-default levels
x2.l = 0.333333333333333;
x3.l = 0.333333333333333;
x4.l = 0.333333333333333;
x5.l = 2;
x6.l = 1;
x7.l = 1;

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;