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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex7_2_4

Formats ams gms mod nl osil
Primal Bounds
3.91801023 p1 ( gdx sol )
(infeas: 3e-10)
Dual Bounds
3.91800892 (ANTIGONE)
3.91800659 (BARON)
3.91801023 (COUENNE)
3.91800957 (LINDO)
3.91800609 (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.
Dembo, R S, A Set of Geometric Programming Test Problems and Their Solutions, Mathematical Programming, 10:1, 1976, 192-213.
Source Test Problem ex7.2.4 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 signomial
Objective curvature indefinite
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 4
#Linear Constraints 0
#Quadratic Constraints 2
#Polynomial Constraints 0
#Signomial Constraints 2
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 13
#Nonlinear Nonzeros in Jacobian 10
#Nonzeros in (Upper-Left) Hessian of Lagrangian 24
#Nonzeros in Diagonal of Hessian of Lagrangian 8
#Blocks in Hessian of Lagrangian 2
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
Infeasibility of initial point 105.7
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        1        0        4        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
*         18        4       14        0
*
*  Solve m using NLP minimizing objvar;


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

Equations  e1,e2,e3,e4,e5;


e1.. -(0.4*x1**0.67/x7**0.67 + 0.4*x2**0.67/x8**0.67 - x1 - x2) + objvar =E= 10
     ;

e2.. 0.0588*x5*x7 + 0.1*x1 =L= 1;

e3.. 0.0588*x6*x8 + 0.1*x1 + 0.1*x2 =L= 1;

e4.. 4*x3/x5 + 2/(x3**0.71*x5) + 0.0588*x7/x3**1.3 =L= 1;

e5.. 4*x4/x6 + 2/(x4**0.71*x6) + 0.0588*x4**1.3*x8 =L= 1;

* set non-default bounds
x1.lo = 0.1; x1.up = 10;
x2.lo = 0.1; x2.up = 10;
x3.lo = 0.1; x3.up = 10;
x4.lo = 0.1; x4.up = 10;
x5.lo = 0.1; x5.up = 10;
x6.lo = 0.1; x6.up = 10;
x7.lo = 0.1; x7.up = 10;
x8.lo = 0.1; x8.up = 10;

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
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