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Instance: ex6_2_6

Formats ams gms mod nl osil
Primal Bounds
0.00000071 p1 ( gdx sol )
(infeas: 0)
-0.00000260 p2 ( gdx sol )
(infeas: 2e-14)
Dual Bounds
-0.00001850 (ANTIGONE)
-0.00000260 (BARON)
-0.00009015 (COUENNE)
-0.00000260 (LINDO)
-0.00002171 (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 ex6.2.6 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 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(3.9235*x2 + 6.0909*x3 + 0.92*x4)*(26.9071667605344*x2 + 
     41.7710875549227*x3 + 6.30931398488382*x4) + 0.668686155614739*x2 - 
     1.14374230885457*x3 + 2.8906196099828*x4 + 9.58716676053442*log(x2)*x2 + 
     16.9310875549227*log(x3)*x3 + 0.309313984883821*log(x4)*x4 - 
     9.58716676053442*log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*x2 - 
     16.9310875549227*log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*x3 - 
     0.309313984883821*log(3.9235*x2 + 6.0909*x3 + 0.92*x4)*x4 + 18.32*log(x2)*
     x2 + 25.84*log(x3)*x3 + 7*log(x4)*x4 - 18.32*log(3.664*x2 + 5.168*x3 + 1.4
     *x4)*x2 - 25.84*log(3.664*x2 + 5.168*x3 + 1.4*x4)*x3 - 7*log(3.664*x2 + 
     5.168*x3 + 1.4*x4)*x4 + log(4.0643*x2 + 5.7409*x3 + 1.6741*x4)*(4.0643*x2
      + 5.7409*x3 + 1.6741*x4) + 4.0643*log(x2)*x2 + 5.7409*log(x3)*x3 + 1.6741
     *log(x4)*x4 - 4.0643*log(4.0643*x2 + 3.22644664511275*x3 + 
     1.44980651607875*x4)*x2 - 5.7409*log(5.31147575751424*x2 + 5.7409*x3 + 
     0.00729924451284409*x4)*x3 - 1.6741*log(2.25846661774355*x2 + 
     3.70876916588753*x3 + 1.6741*x4)*x4 - 30.9714667605344*log(x2)*x2 - 
     47.5119875549227*log(x3)*x3 - 7.98341398488382*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 = 0.51802;
x3.l = 0.0511;
x4.l = 0.43088;

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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