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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex6_1_4

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.29454129 p1 ( gdx sol ) (infeas: 1e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.29454354 (ANTIGONE) -0.29454129 (BARON) -0.29454129 (COUENNE) -0.29454135 (LINDO) -0.29454129 (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. McDonald, C M and Floudas, C A, Global Optimization for the Phase and Chemical Equilibrium Problem: Application to the NRTL Equation, Computers and Chemical Engineering, 19:11, 1995, 1111-1139.
Sourceⓘ	Test Problem ex6.1.4 of Chapter 6 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ⓘ	indefinite
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	4
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	log mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	15
#Nonlinear Nonzeros in Jacobianⓘ	12
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	21
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#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ⓘ	3.4723e-02
Maximal coefficientⓘ	1.4481e+00
Infeasibility of initial pointⓘ	1.11e-16
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
*         22        4       18        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x5,x6,x7;

Equations  e1,e2,e3,e4,e5;


e1.. -((0.28809 + log(x2))*x2 + (-0.29158 + log(x3))*x3 + (0.59336 + log(x4))*
     x4 + x2*(1.44805026165593*x6 + 0.989428667054834*x7) + x3*(
     1.12676386427658*x5 + 1.00363012835441*x7) + x4*(0.0347225450624344*x5 + 
     0.82681418300153*x6)) + objvar =E= 0;

e2.. x5*(x2 + 0.145002897355373*x3 + 0.989528214945409*x4) - x2 =E= 0;

e3.. x6*(0.293701311601799*x2 + x3 + 0.646291923054068*x4) - x3 =E= 0;

e4.. x7*(0.619143628558899*x2 + 0.239837817616513*x3 + x4) - x4 =E= 0;

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

* set non-default bounds
x2.lo = 1E-6; x2.up = 1;
x3.lo = 1E-6; x3.up = 1;
x4.lo = 1E-6; x4.up = 1;

* set non-default levels
x2.l = 7E-5;
x3.l = 0.99686;
x4.l = 0.00307;
x5.l = 0.000474076675116379;
x6.l = 0.997993046160137;
x7.l = 0.0126755759820888;

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;