MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex4_1_8

Formats ams gms mod nl osil pip
Primal Bounds
-16.73889318 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-16.73889366 (ANTIGONE)
-16.73889472 (BARON)
-16.73889318 (COUENNE)
-16.73889318 (LINDO)
-16.73889388 (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.
Soland, R M, An Algorithm for Separable Nonconvex Programming Problems II: Nonconvex Constraints, Management Science, 17:11, 1971, 759-773.
Source Test Problem ex4.1.8 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 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 1
#Constraints 1
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 1
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 2
#Nonlinear Nonzeros in Jacobian 1
#Nonzeros in (Upper-Left) Hessian of Lagrangian 2
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#Blocks in Hessian of Lagrangian 2
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
Infeasibility of initial point 5.095e-05
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
*          2        2        0        0        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
*          5        3        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Positive Variables  x1,x2;

Equations  e1,e2;


e1.. -(sqr(x2) - 7*x2) + 12*x1 + objvar =E= 0;

e2.. -2*POWER(x1,4) - x2 =E= -2;

* set non-default bounds
x1.up = 2;
x2.up = 3;

* set non-default levels
x1.l = 0.7175;
x2.l = 1.47;

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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