MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex4_1_9

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-5.50801327 p1 ( gdx sol ) (infeas: 5e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-5.50801338 (ANTIGONE) -5.50801329 (BARON) -5.50805570 (COUENNE) -5.50801327 (LINDO) -5.50801353 (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.
Sourceⓘ	Test Problem ex4.1.9 of Chapter 4 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	2
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	1
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	2
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	2
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	nonconvex
#Nonzeros in Jacobianⓘ	4
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	1
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
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
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	9.6000e+01
Infeasibility of initial pointⓘ	0.0001318
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        1        0        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        5        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Positive Variables  x1,x2;

Equations  e1,e2,e3;


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

e2.. 8*POWER(x1,3) - 2*POWER(x1,4) - 8*sqr(x1) + x2 =L= 2;

e3.. 32*POWER(x1,3) - 4*POWER(x1,4) - 88*sqr(x1) + 96*x1 + x2 =L= 36;

* set non-default bounds
x1.up = 3;
x2.up = 4;

* set non-default levels
x1.l = 2.3295;
x2.l = 3.17846;

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;