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Instance mathopt3

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.00000000 p1 ( gdx sol )
(infeas: 3e-17)
Other points (infeas > 1e-08)  
Dual Bounds
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 mathopt3
Application Test Problem
Added to library 31 Jul 2001
Problem type NLP
#Variables 6
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 6
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature nonconcave
#Nonzeros in Objective 6
#Nonlinear Nonzeros in Objective 6
#Constraints 7
#Linear Constraints 3
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 3
Operands in Gen. Nonlin. Functions cos mul sin sqr
Constraints curvature indefinite
#Nonzeros in Jacobian 36
#Nonlinear Nonzeros in Jacobian 18
#Nonzeros in (Upper-Left) Hessian of Lagrangian 36
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 6
Maximal blocksize in Hessian of Lagrangian 6
Average blocksize in Hessian of Lagrangian 6.0
#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 1089
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
*          8        5        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         43       19       24        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1.. -(sqr(x1 + x2) + sqr(x3 - x5) + sqr(x6 - x4) + 2*sqr(x1 + x3 - x4) + sqr(
     x2 - x1 + x3 - x4) + 10*sqr(sin(x1 + x5 - x6))) + objvar =E= 0;

e2.. sqr(x1) - sin(x2) - x4 + x5 + x6 =E= 0;

e3.. x1*x3 - x2*x4*x1 - sin((-x1) - x3 + x6) - x5 =E= 0;

e4.. x2*x6*cos(x5) - sin(x3*x4) + x2 - x5 =E= 0;

e5.. x1*x2 - sqr(x3) - x4*x5 - sqr(x6) =E= 0;

e6..    2*x1 + 5*x2 + x3 + x4 =L= 1;

e7..    3*x1 - 2*x2 + x3 - 4*x4 =L= 0;

e8..    x1 + x2 + x3 + x4 + x5 + x6 =L= 2;

* set non-default levels
x1.l = 10;
x2.l = -10;
x3.l = 10;
x4.l = 10;
x5.l = 10;
x6.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;


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