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Instance: ex6_2_11

Formats ams gms mod nl osil
Primal Bounds
-0.00000267 p1 ( gdx sol )
(infeas: 2e-16)
Dual Bounds
-0.00000685 (ANTIGONE)
-0.00000267 (BARON)
-0.00044799 (COUENNE)
-0.00000267 (LINDO)
-0.00239605 (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, Global Optimization for the Phase and Chemical Equilibrium Problem, PhD thesis, Princeton University, 1995.
Source Test Problem ex6.2.11 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 mul div log
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
Infeasibility of initial point 0
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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(2.1055*x2 + 3.1878*x3 + 0.92*x4)*(15.3261663216011*x2 + 
     23.2043471859416*x3 + 6.69678129464404*x4) + 1.04055250396734*x2 - 
     2.24199441248417*x3 + 3.1618173099828*x4 + 6.4661663216011*log(x2/(2.1055*
     x2 + 3.1878*x3 + 0.92*x4))*x2 + 12.2043471859416*log(x3/(2.1055*x2 + 
     3.1878*x3 + 0.92*x4))*x3 + 0.696781294644034*log(x4/(2.1055*x2 + 3.1878*x3
      + 0.92*x4))*x4 + 9.86*log(x2/(1.972*x2 + 2.4*x3 + 1.4*x4))*x2 + 12*log(x3
     /(1.972*x2 + 2.4*x3 + 1.4*x4))*x3 + 7*log(x4/(1.972*x2 + 2.4*x3 + 1.4*x4))
     *x4 + log(1.972*x2 + 2.4*x3 + 1.4*x4)*(1.972*x2 + 2.4*x3 + 1.4*x4) + 1.972
     *log(x2/(1.972*x2 + 0.283910843616504*x3 + 3.02002220174195*x4))*x2 + 2.4*
     log(x3/(1.45991339466884*x2 + 2.4*x3 + 0.415073537580851*x4))*x3 + 1.4*
     log(x4/(0.602183324335333*x2 + 0.115623371371275*x3 + 1.4*x4))*x4 - 
     17.2981663216011*log(x2)*x2 - 25.6043471859416*log(x3)*x3 - 
     8.09678129464404*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 = 0.00565;
x3.l = 0.99054;
x4.l = 0.00381;

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;


Last updated: 2018-09-14 Git hash: ac5a5314
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