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Instance: ex6_2_7

Formats ams gms mod nl osil
Primal Bounds
-0.16084762 p1 ( gdx sol )
(infeas: 6e-17)
Dual Bounds
-4.58704966 (ANTIGONE)
-1.06726714 (BARON)
-8.49978555 (COUENNE)
-2.79052621 (LINDO)
-8.80022512 (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, GLOPEQ: A New Computational Tool for the Phase and Chemical Equilibrium Problem, Computers and Chemical Engineering, 21:1, 1997, 1-23.
Source Test Problem ex6.2.7 of Chapter 6 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 9
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 9
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 9
#Nonlinear Nonzeros in Objective 9
#Constraints 3
#Linear Constraints 3
#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 9
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 27
#Nonzeros in Diagonal of Hessian of Lagrangian 9
#Blocks in Hessian of Lagrangian 3
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
*          4        4        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         10       10        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         19       10        9        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10;

Equations  e1,e2,e3,e4;


e1.. -(log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*(10.4807341082197*x2 + 
     38.5043409542885*x5 + 8.73945638067505*x8) + 0.102582206615077*x2 - 
     4.55292602721008*x5 + 0.0196376909050935*x8 + 0.240734108219679*log(x2)*x2
      + 2.64434095428848*log(x5)*x5 + 0.399456380675047*log(x8)*x8 - 
     0.240734108219679*log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*x2 - 
     2.64434095428848*log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*x5 - 
     0.399456380675047*log(2.4088*x2 + 8.8495*x5 + 2.0086*x8)*x8 + 11.24*log(x2
     )*x2 + 36.86*log(x5)*x5 + 9.34*log(x8)*x8 - 11.24*log(2.248*x2 + 7.372*x5
      + 1.868*x8)*x2 - 36.86*log(2.248*x2 + 7.372*x5 + 1.868*x8)*x5 - 9.34*log(
     2.248*x2 + 7.372*x5 + 1.868*x8)*x8 + log(2.248*x2 + 7.372*x5 + 1.868*x8)*(
     2.248*x2 + 7.372*x5 + 1.868*x8) + 2.248*log(x2)*x2 + 7.372*log(x5)*x5 + 
     1.868*log(x8)*x8 - 2.248*log(2.248*x2 + 5.82088173817021*x5 + 
     0.382446861901943*x8)*x2 - 7.372*log(0.972461133672523*x2 + 7.372*x5 + 
     1.1893141713454*x8)*x5 - 1.868*log(1.86752460515164*x2 + 2.61699842799583*
     x5 + 1.868*x8)*x8 + log(2.4088*x3 + 8.8495*x6 + 2.0086*x9)*(
     10.4807341082197*x3 + 38.5043409542885*x6 + 8.73945638067505*x9) + 
     0.102582206615077*x3 - 4.55292602721008*x6 + 0.0196376909050935*x9 + 
     0.240734108219679*log(x3)*x3 + 2.64434095428848*log(x6)*x6 + 
     0.399456380675047*log(x9)*x9 - 0.240734108219679*log(2.4088*x3 + 8.8495*x6
      + 2.0086*x9)*x3 - 2.64434095428848*log(2.4088*x3 + 8.8495*x6 + 2.0086*x9)
     *x6 - 0.399456380675047*log(2.4088*x3 + 8.8495*x6 + 2.0086*x9)*x9 + 11.24*
     log(x3)*x3 + 36.86*log(x6)*x6 + 9.34*log(x9)*x9 - 11.24*log(2.248*x3 + 
     7.372*x6 + 1.868*x9)*x3 - 36.86*log(2.248*x3 + 7.372*x6 + 1.868*x9)*x6 - 
     9.34*log(2.248*x3 + 7.372*x6 + 1.868*x9)*x9 + log(2.248*x3 + 7.372*x6 + 
     1.868*x9)*(2.248*x3 + 7.372*x6 + 1.868*x9) + 2.248*log(x3)*x3 + 7.372*log(
     x6)*x6 + 1.868*log(x9)*x9 - 2.248*log(2.248*x3 + 5.82088173817021*x6 + 
     0.382446861901943*x9)*x3 - 7.372*log(0.972461133672523*x3 + 7.372*x6 + 
     1.1893141713454*x9)*x6 - 1.868*log(1.86752460515164*x3 + 2.61699842799583*
     x6 + 1.868*x9)*x9 + log(2.4088*x4 + 8.8495*x7 + 2.0086*x10)*(
     10.4807341082197*x4 + 38.5043409542885*x7 + 8.73945638067505*x10) + 
     0.102582206615077*x4 - 4.55292602721008*x7 + 0.0196376909050935*x10 + 
     0.240734108219679*log(x4)*x4 + 2.64434095428848*log(x7)*x7 + 
     0.399456380675047*log(x10)*x10 - 0.240734108219679*log(2.4088*x4 + 8.8495*
     x7 + 2.0086*x10)*x4 - 2.64434095428848*log(2.4088*x4 + 8.8495*x7 + 2.0086*
     x10)*x7 - 0.399456380675047*log(2.4088*x4 + 8.8495*x7 + 2.0086*x10)*x10 + 
     11.24*log(x4)*x4 + 36.86*log(x7)*x7 + 9.34*log(x10)*x10 - 11.24*log(2.248*
     x4 + 7.372*x7 + 1.868*x10)*x4 - 36.86*log(2.248*x4 + 7.372*x7 + 1.868*x10)
     *x7 - 9.34*log(2.248*x4 + 7.372*x7 + 1.868*x10)*x10 + log(2.248*x4 + 7.372
     *x7 + 1.868*x10)*(2.248*x4 + 7.372*x7 + 1.868*x10) + 2.248*log(x4)*x4 + 
     7.372*log(x7)*x7 + 1.868*log(x10)*x10 - 2.248*log(2.248*x4 + 
     5.82088173817021*x7 + 0.382446861901943*x10)*x4 - 7.372*log(
     0.972461133672523*x4 + 7.372*x7 + 1.1893141713454*x10)*x7 - 1.868*log(
     1.86752460515164*x4 + 2.61699842799583*x7 + 1.868*x10)*x10 - 
     12.7287341082197*log(x2)*x2 - 45.8763409542885*log(x5)*x5 - 
     10.607456380675*log(x8)*x8 - 12.7287341082197*log(x3)*x3 - 
     45.8763409542885*log(x6)*x6 - 10.607456380675*log(x9)*x9 - 
     12.7287341082197*log(x4)*x4 - 45.8763409542885*log(x7)*x7 - 
     10.607456380675*log(x10)*x10) + objvar =E= 0;

e2..    x2 + x3 + x4 =E= 0.4;

e3..    x5 + x6 + x7 =E= 0.1;

e4..    x8 + x9 + x10 =E= 0.5;

* set non-default bounds
x2.lo = 1E-7; x2.up = 0.4;
x3.lo = 1E-7; x3.up = 0.4;
x4.lo = 1E-7; x4.up = 0.4;
x5.lo = 1E-7; x5.up = 0.1;
x6.lo = 1E-7; x6.up = 0.1;
x7.lo = 1E-7; x7.up = 0.1;
x8.lo = 1E-7; x8.up = 0.5;
x9.lo = 1E-7; x9.up = 0.5;
x10.lo = 1E-7; x10.up = 0.5;

* set non-default levels
x2.l = 0.0088;
x3.l = 0.33595;
x4.l = 0.05525;
x5.l = 0.00065;
x6.l = 0.00193;
x7.l = 0.09742;
x8.l = 0.30803;
x9.l = 0.147;
x10.l = 0.04497;

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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