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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 py
Primal Bounds (infeas ≤ 1e-08)ⓘ	3.91801023 p1 ( gdx sol ) (infeas: 3e-10)
Other points (infeas > 1e-08)ⓘ
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
Minimal coefficientⓘ	5.8800e-02
Maximal coefficientⓘ	4.0000e+00
Infeasibility of initial pointⓘ	105.7
Sparsity Jacobianⓘ
Sparsity 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;