MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: ex8_5_5

Formats ams gms mod nl osil
Primal Bounds
-0.01075334 p1 ( gdx sol )
(infeas: 1e-11)
Dual Bounds
-0.01075334 (COUENNE)
-0.01075374 (LINDO)
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 ex8.5.5 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 5
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 5
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature unknown
#Nonzeros in Objective 5
#Nonlinear Nonzeros in Objective 5
#Constraints 4
#Linear Constraints 2
#Quadratic Constraints 1
#Polynomial Constraints 1
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions mul div log
Constraints curvature indefinite
#Nonzeros in Jacobian 11
#Nonlinear Nonzeros in Jacobian 5
#Nonzeros in (Upper-Left) Hessian of Lagrangian 12
#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 3
Average blocksize in Hessian of Lagrangian 2.5
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17        7       10        0
*
*  Solve m using NLP minimizing objvar;


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

Equations  e1,e2,e3,e4,e5;


e1.. -(log(x2)*x2 + log(x3)*x3 - log(x4 - x6) + x4 - 0.353553390593274*log((x4
      + 2.41421356237309*x6)/(x4 - 0.414213562373095*x6))*x5/x6 + 
     2.5746329124341*x2 + 0.54639755131421*x3) + objvar =E= -1;

e2.. POWER(x4,3) - sqr(x4)*(1 - x6) + (-3*sqr(x6) - 2*x6 + x5)*x4 - x5*x6 + 
     POWER(x6,3) + sqr(x6) =E= 0;

e3.. -(0.884831*x2*x2 + 0.555442*x2*x3 + 0.555442*x3*x2 + 0.427888*x3*x3) + x5
      =E= 0;

e4..  - 0.0885973*x2 - 0.0890893*x3 + x6 =E= 0;

e5..    x2 + x3 =E= 1;

* set non-default levels
x2.l = 0.5;
x3.l = 0.5;
x4.l = 2;
x5.l = 1;
x6.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;


Last updated: 2018-09-14 Git hash: ac5a5314
Imprint / Privacy Policy