MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex8_5_1

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.00000041 p1 ( gdx sol ) (infeas: 1e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.31496449 (COUENNE) -0.00000127 (LINDO) -0.00000565 (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. Green, K, Zhou, S, and Luks, K, The Fractal Response of Robust Solution Techniques to the Stationary Point Problem, Fluid Phase Equilibria, 84, 1993, 49-78.
Sourceⓘ	Test Problem ex8.5.1 of Chapter 8 of Floudas e.a. handbook
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ⓘ	unknown
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	4
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	div log mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	14
#Nonlinear Nonzeros in Jacobianⓘ	6
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	17
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	5
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.4998e-01
Maximal coefficientⓘ	3.8008e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          5        5        0        0        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
*         21        9       12        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7;

Positive Variables  x2,x3,x4,x5;

Equations  e1,e2,e3,e4,e5;


e1.. -(log(x2)*x2 + log(x3)*x3 + log(x4)*x4 + x7/(x5 - x7) - log(x5 - x7) - 2*
     x6/x5 + 0.430983578191493*x2 + 3.80082402249182*x3 + 2.92297302249182*x4)
      + objvar =E= 0;

e2.. POWER(x5,3) - sqr(x5)*(1 + x7) + x6*x5 - x6*x7 =E= 0;

e3.. -(0.37943*x2*x2 + 0.75885*x2*x3 + 0.48991*x2*x4 + 0.75885*x3*x2 + 0.8836*
     x3*x3 + 0.23612*x3*x4 + 0.48991*x4*x2 + 0.23612*x4*x3 + 0.63263*x4*x4)
      + x6 =E= 0;

e4..  - 0.14998*x2 - 0.14998*x3 - 0.14998*x4 + x7 =E= 0;

e5..    x2 + x3 + x4 =E= 1;

* set non-default levels
x2.l = 0.333333333333333;
x3.l = 0.333333333333333;
x4.l = 0.333333333333333;
x5.l = 2;
x6.l = 1;
x7.l = 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;