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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: mathopt5_3

Formats ams gms mod nl osil
Primal Bounds (infeas ≤ 1e-08)
-1.61642493 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-1.61642493 (COUENNE)
-1.61642495 (LINDO)
References Mathematica, MathOptimizer - An Advanced Modeling and Optimization System for Mathematica Users.
Pinter, J D, Global Optimization in Action - Continuous and Lipschitz Optimization: Algorithms, Implementations, and Applications, Kluwer Acadameic Publishers, 1996.
Pinter, J D, Computational Global Optimization in Nonlinear Systems - An Interactive Tutorial, Lionheart Publishing, Atlanta, GA, 2001.
Source GAMS Model Library model mathopt5, function f3
Application Test Problem
Added to library 18 Aug 2014
Problem type NLP
#Variables 1
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 1
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature nonconvex
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 1
#Constraints 0
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions mul cos sin sqr
Constraints curvature linear
#Nonzeros in Jacobian 0
#Nonlinear Nonzeros in Jacobian 0
#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
Infeasibility of initial point 0
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
*          1        1        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          2        2        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          2        1        1        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,objvar;

Positive Variables  x1;

Equations  e1;


e1.. -sin(x1)*sqr(cos(x1) - sin(x1)) + objvar =E= 0;

* set non-default bounds
x1.up = 10;

* set non-default levels
x1.l = 3;

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: 2019-06-04 Git hash: 78444eaa
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