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Instance: ex8_5_6

Formats ams gms mod nl osil
Primal Bounds
0.00000099 p1 ( gdx sol )
(infeas: 2e-14)
-0.00116737 p2 ( gdx sol )
(infeas: 2e-12)
Dual Bounds
-5.64397282 (COUENNE)
-0.00116848 (LINDO)
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.
Hua, J, Brennecke, J, and Stadtherr, M, Enhanced Interval Analysis for Phase Stability: Cubic Equation of State Models, Industrial and Engineering Chemistry Research, 37:4, 1998, 1519-1527.
Source Test Problem ex8.5.6 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 mul div log
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
Infeasibility of initial point 1
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
*          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;

Equations  e1,e2,e3,e4,e5;


e1.. -(log(x2)*x2 + log(x3)*x3 + log(x4)*x4 - log(x5 - x7) + x5 - 
     0.353553390593274*log((x5 + 2.41421356237309*x7)/(x5 - 0.414213562373095*
     x7))*x6/x7 + 1.42876598488588*x2 + 1.27098480432594*x3 + 1.62663700075562*
     x4) + objvar =E= -1;

e2.. POWER(x5,3) - sqr(x5)*(1 - x7) + (-3*sqr(x7) - 2*x7 + x6)*x5 - x6*x7 + 
     POWER(x7,3) + sqr(x7) =E= 0;

e3.. -(0.142724*x2*x2 + 0.206577*x2*x3 + 0.342119*x2*x4 + 0.206577*x3*x2 + 
     0.323084*x3*x3 + 0.547748*x3*x4 + 0.342119*x4*x2 + 0.547748*x4*x3 + 
     0.968906*x4*x4) + x6 =E= 0;

e4..  - 0.0815247*x2 - 0.0907391*x3 - 0.13705*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;


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