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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex14_1_4

Formats ams gms mod nl osil
Primal Bounds
-0.00000000 p1 ( gdx sol )
(infeas: 9e-17)
Dual Bounds
-0.00000000 (COUENNE)
-0.00000000 (LINDO)
References Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999.
Ferraris, G B and Tronconi, E, BUNLSI - a FORTRAN Program for Solution of Systems of Nonlinear Algebraic Equations, Computers and Chemical Engineering, 10:2, 1986, 129-141.
Source Test Problem ex14.1.4 of Chapter 14 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 3
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 4
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 4
Operands in Gen. Nonlin. Functions mul sin exp
Constraints curvature indefinite
#Nonzeros in Jacobian 12
#Nonlinear Nonzeros in Jacobian 6
#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
Infeasibility of initial point 1.046
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
*          5        1        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          4        4        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         14        8        6        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,objvar;

Equations  e1,e2,e3,e4,e5;


e1.. 0.5*sin(x1*x2) - 0.5*x1 - 0.0795774703703634*x2 - x3 =L= 0;

e2.. 0.920422529629637*exp(2*x1) - 5.4365636*x1 + 0.865255957591193*x2 - x3
      =L= 2.5019678106022;

e3.. 0.5*x1 - 0.5*sin(x1*x2) + 0.0795774703703634*x2 - x3 =L= 0;

e4..  - x3 + objvar =E= 0;

e5.. 5.4365636*x1 - 0.920422529629637*exp(2*x1) - 0.865255957591193*x2 - x3
      =L= -2.5019678106022;

* set non-default bounds
x1.lo = 0.25; x1.up = 1;
x2.lo = 1.5; x2.up = 6.28;

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;


Last updated: 2018-09-14 Git hash: ac5a5314
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