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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 py
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) -1.61642548 (SCIP)
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ⓘ	cos mul 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 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;