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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex6_2_8

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.02700635 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.02701481 (ANTIGONE) -0.02700635 (BARON) -0.02704771 (COUENNE) -0.02700791 (LINDO) -0.02700731 (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 Stability Problem, AIChE Journal, 41:7, 1995, 1798-1814.
Sourceⓘ	Test Problem ex6.2.8 of Chapter 6 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	1
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	log mul
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	3
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	4.2358e-02
Maximal coefficientⓘ	4.5876e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        2        0        0        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
*          7        4        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4;

Equations  e1,e2;


e1.. -(log(2.4088*x2 + 8.8495*x3 + 2.0086*x4)*(10.4807341082197*x2 + 
     38.5043409542885*x3 + 8.73945638067505*x4) + 0.303602206615077*x2 - 
     3.98949602721008*x3 + 0.0423576909050935*x4 + 0.240734108219679*log(x2)*x2
      + 2.64434095428848*log(x3)*x3 + 0.399456380675047*log(x4)*x4 - 
     0.240734108219679*log(2.4088*x2 + 8.8495*x3 + 2.0086*x4)*x2 - 
     2.64434095428848*log(2.4088*x2 + 8.8495*x3 + 2.0086*x4)*x3 - 
     0.399456380675047*log(2.4088*x2 + 8.8495*x3 + 2.0086*x4)*x4 + 11.24*log(x2
     )*x2 + 36.86*log(x3)*x3 + 9.34*log(x4)*x4 - 11.24*log(2.248*x2 + 7.372*x3
      + 1.868*x4)*x2 - 36.86*log(2.248*x2 + 7.372*x3 + 1.868*x4)*x3 - 9.34*log(
     2.248*x2 + 7.372*x3 + 1.868*x4)*x4 + log(2.248*x2 + 7.372*x3 + 1.868*x4)*(
     2.248*x2 + 7.372*x3 + 1.868*x4) + 2.248*log(x2)*x2 + 7.372*log(x3)*x3 + 
     1.868*log(x4)*x4 - 2.248*log(2.248*x2 + 5.82088173817021*x3 + 
     0.382446861901943*x4)*x2 - 7.372*log(0.972461133672523*x2 + 7.372*x3 + 
     1.1893141713454*x4)*x3 - 1.868*log(1.86752460515164*x2 + 2.61699842799583*
     x3 + 1.868*x4)*x4 - 12.7287341082197*log(x2)*x2 - 45.8763409542885*log(x3)
     *x3 - 10.607456380675*log(x4)*x4) + objvar =E= 0;

e2..    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 = 0.7154;
x3.l = 0.00336;
x4.l = 0.28124;

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;