MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: ex1223

Formats ams gms mod nl osil
Primal Bounds
4.57958240 p1 ( gdx sol )
(infeas: 9e-16)
Dual Bounds
4.57958240 (ALPHAECP)
4.57958240 (ANTIGONE)
4.57958240 (BARON)
4.57958240 (BONMIN)
4.57958240 (COUENNE)
4.57958240 (LINDO)
4.57958240 (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.
Yuan, X, Zhang, S, Pibouleau, L, and Domenech, S, Une méthode d'optimisation non linéaire en variables mixtes pour la conception de procédés, RAIRO - Operations Research, 22:4, 1988, 331-346.
Source Test Problem ex12.2.3 of Chapter 12 of Floudas e.a. handbook
Added to library 01 May 2001
Problem type MBNLP
#Variables 11
#Binary Variables 4
#Integer Variables 0
#Nonlinear Variables 7
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature convex
#Nonzeros in Objective 7
#Nonlinear Nonzeros in Objective 7
#Constraints 13
#Linear Constraints 9
#Quadratic Constraints 4
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions sqr log
Constraints curvature convex
#Nonzeros in Jacobian 32
#Nonlinear Nonzeros in Jacobian 10
#Nonzeros in (Upper-Left) Hessian of Lagrangian 7
#Nonzeros in Diagonal of Hessian of Lagrangian 7
#Blocks in Hessian of Lagrangian 7
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0
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
*         14        5        0        9        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         12        8        4        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         40       23       17        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,b8,b9,b10,b11,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7;

Binary Variables  b8,b9,b10,b11;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14;


e1..    x1 + x2 + x3 + b8 + b9 + b10 =L= 5;

e2.. sqr(x6) + sqr(x1) + sqr(x2) + sqr(x3) =L= 5.5;

e3..    x1 + b8 =L= 1.2;

e4..    x2 + b9 =L= 1.8;

e5..    x3 + b10 =L= 2.5;

e6..    x1 + b11 =L= 1.2;

e7.. sqr(x5) + sqr(x2) =L= 1.64;

e8.. sqr(x6) + sqr(x3) =L= 4.25;

e9.. sqr(x5) + sqr(x3) =L= 4.64;

e10..    x4 - b8 =E= 0;

e11..    x5 - b9 =E= 0;

e12..    x6 - b10 =E= 0;

e13..    x7 - b11 =E= 0;

e14.. -(sqr((-1) + x4) + sqr((-2) + x5) + sqr((-1) + x6) - log(1 + x7) + sqr((-
      1) + x1) + sqr((-2) + x2) + sqr((-3) + x3)) + objvar =E= 0;

* set non-default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


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