MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex14_1_8

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.04141589 p1 ( gdx sol ) (infeas: 0) 0.00000000 p2 ( gdx sol ) (infeas: 2e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) 0.00000000 (BARON) 0.00000000 (COUENNE) -0.00000000 (LINDO) 0.00000000 (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. Kubíček, M, Hofmann, H, Hlaváček, V, and Sinkule, J, Multiplicity and Stability in a Sequence of Two Nonadiabatic Nonisothermal CSTRS, Chemical Engineering Science, 35:4, 1980, 987-996.
Sourceⓘ	Test Problem ex14.1.8 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ⓘ	div exp mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	10
#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ⓘ	1.0000e-02
Maximal coefficientⓘ	1.0000e+01
Infeasibility of initial pointⓘ	0.143
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
*         12        6        6        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,objvar;

Positive Variables  x1,x2;

Equations  e1,e2,e3,e4,e5;


e1..  - x3 + objvar =E= 0;

e2.. exp(10*x1/(1 + 0.01*x1))*(0.0476666666666666 - 0.0649999999999999*x1) - x1
      - x3 =L= 0;

e3.. x1 - exp(10*x1/(1 + 0.01*x1))*(0.0476666666666666 - 0.0649999999999999*x1)
      - x3 =L= 0;

e4.. exp(10*x2/(1 + 0.01*x2))*(0.143 - 0.13*x1 - 0.195*x2) + x1 - 3*x2 - x3
      =L= 0;

e5.. (-exp(10*x2/(1 + 0.01*x2))*(0.143 - 0.13*x1 - 0.195*x2)) - x1 + 3*x2 - x3
      =L= 0;

* set non-default bounds
x1.up = 1;
x2.up = 1;

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;