MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance ex7_3_2

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.08986397 p1 ( gdx sol ) (infeas: 8e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1.08986397 (ANTIGONE) 1.08986397 (BARON) 1.08986397 (COUENNE) 1.08986397 (LINDO) 1.08986391 (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. Sideris, A and Sanchez Pena, R S, Fast Computation of the Multivariable Stability Margin for Real Interrelated Uncertain Parameters, IEEE Transactions on Automatic Control, 34:12, 1989, 1272-1276.
Sourceⓘ	Test Problem ex7.3.2 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	7
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	15
#Nonlinear Nonzeros in Jacobianⓘ	3
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	6
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.0000e-01
Maximal coefficientⓘ	4.0000e+00
Infeasibility of initial pointⓘ	1.5
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        1        0        7        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17       14        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1..  - x4 + objvar =E= 0;

e2.. POWER(x1,4)*POWER(x2,4) - POWER(x1,4) - POWER(x2,4)*x3 =L= 0;

e3..  - x1 - 0.25*x4 =L= -1.4;

e4..    x1 - 0.25*x4 =L= 1.4;

e5..  - x2 - 0.2*x4 =L= -1.5;

e6..    x2 - 0.2*x4 =L= 1.5;

e7..  - x3 - 0.2*x4 =L= -0.8;

e8..    x3 - 0.2*x4 =L= 0.8;

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;