MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: ex7_2_3

Formats ams gms mod nl osil
Primal Bounds
7049.24802000 p1 ( gdx sol )
(infeas: 3e-10)
Dual Bounds
7049.22780700 (ANTIGONE)
2298.35669700 (BARON)
2238.62632800 (COUENNE)
7049.24802000 (LINDO)
3480.49720100 (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.
Avriel, M and Williams, A C, An Extension of Geometric Programming with Applications in Engineering Optimization, Journal of Engineering Mathematics, 5:2, 1971, 187-194.
Source Test Problem ex7.2.3 of Chapter 7 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 8
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 0
#Constraints 6
#Linear Constraints 3
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 3
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 17
#Nonlinear Nonzeros in Jacobian 10
#Nonzeros in (Upper-Left) Hessian of Lagrangian 28
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 8
Maximal blocksize in Hessian of Lagrangian 8
Average blocksize in Hessian of Lagrangian 8.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 122.5
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
*          7        1        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          9        9        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         21       11       10        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7;


e1..  - x1 - x2 - x3 + objvar =E= 0;

e2.. 833.33252*x4/x1/x6 + 100/x6 - 83333.333/(x1*x6) =L= 1;

e3.. 1250*x5/x2/x7 + x4/x7 - 1250*x4/x2/x7 =L= 1;

e4.. 1250000/(x3*x8) + x5/x8 - 2500*x5/x3/x8 =L= 1;

e5..    0.0025*x4 + 0.0025*x6 =L= 1;

e6..  - 0.0025*x4 + 0.0025*x5 + 0.0025*x7 =L= 1;

e7..  - 0.01*x5 + 0.01*x8 =L= 1;

* set non-default bounds
x1.lo = 100; x1.up = 10000;
x2.lo = 1000; x2.up = 10000;
x3.lo = 1000; x3.up = 10000;
x4.lo = 10; x4.up = 1000;
x5.lo = 10; x5.up = 1000;
x6.lo = 10; x6.up = 1000;
x7.lo = 10; x7.up = 1000;
x8.lo = 10; x8.up = 1000;

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