MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance trigx

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.09563139 p1 ( gdx sol ) (infeas: 7e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.09563139 (COUENNE) 0.09563139 (LINDO) 0.09563103 (SCIP)
Referencesⓘ	Pinter, J D, Nonlinear optimization with GAMS/LGO, Journal of Global Optimization, 38:1, 2007, 79-101.
Sourceⓘ	GAMS Model Library model trigx
Applicationⓘ	Test Problem
Added to libraryⓘ	18 Aug 2014
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ⓘ	2
#Constraintsⓘ	2
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	2
Operands in Gen. Nonlin. Functionsⓘ	cos sin
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	4
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.0000e+00
Maximal coefficientⓘ	5.0000e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        3        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
*          7        1        6        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3;

Equations  e1,e2,e3;


e1.. -(x2*x2 + x3*x3) + objvar =E= 0;

e2.. x2 - sin(2*x2 + 3*x3) - cos(3*x2 - 5*x3) =E= 0;

e3.. x3 - sin(x2 - 2*x3) + cos(x2 + 3*x3) =E= 0;

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;