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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance mathopt2

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 4e-17)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) -0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (LINDO) 0.00000000 (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 mathopt2
Applicationⓘ	Test Problem
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ⓘ	polynomial
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	4
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	8
#Nonlinear Nonzeros in Jacobianⓘ	2
#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ⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+01
Infeasibility of initial pointⓘ	210
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          5        3        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
*         11        7        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Equations  e1,e2,e3,e4,e5;


e1.. -(sqr(2*sqr(x1) - x2) + sqr(x2 - 6*sqr(x1))) + objvar =E= 0;

e2.. x1 - (x1*x2 + 10*x2) =E= 0;

e3..    x1 - 3*x2 =E= 0;

e4..    x1 + x2 =L= 1;

e5..  - x1 + x2 =L= 2;

* set non-default levels
x1.l = 10;
x2.l = -10;

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;