MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex14_1_4

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0. p1 ( gdx sol ) (infeas: 9e-17)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0. (COUENNE) -0. (LINDO) -0. (SCIP)
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ⓘ	exp mul sin
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
Minimal coefficientⓘ	7.9577e-02
Maximal coefficientⓘ	5.4366e+00
Infeasibility of initial pointⓘ	1.046
Sparsity Jacobianⓘ
Sparsity 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;