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Instance mathopt6

The Hundred-dollar, Hundred-digit Challenge Problems as stated by N. Trefethen, Oxford University.

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.26556590 p1 ( gdx sol ) (infeas: 0) -1.29529771 p2 ( gdx sol ) (infeas: 0) -3.30686782 p3 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-3.30686865 (COUENNE) -3.30686866 (LINDO) -3.30686941 (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. Trefethen, N, A Hundred-dollar, Hundred-digit Challenge, SIAM News, 35:1, 2002.
Sourceⓘ	GAMS Model Library model mathopt6
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ⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	0
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	exp sin sqr
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	0
#Nonlinear Nonzeros in Jacobianⓘ	0
#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ⓘ	2.5000e-01
Maximal coefficientⓘ	8.0000e+01
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
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          3        1        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Equations  e1;


e1.. -(exp(sin(50*x1)) + sin(60*exp(x2)) + sin(70*sin(x1)) + sin(sin(80*x2)) - 
     sin(10*x1 + 10*x2) + 0.25*(sqr(x1) + sqr(x2))) + objvar =E= 0;

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

* set non-default levels
x1.l = -0.655668942;
x2.l = 0.346914252;

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;