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Instance ex6_2_5

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-70.75207783 p1 ( gdx sol ) (infeas: 7e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-364.11622330 (ANTIGONE) -111.42017130 (BARON) -477.63328540 (COUENNE) -803.77443220 (LINDO) -492.44034070 (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 ex6.2.5 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ⓘ	div log mul
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
Minimal coefficientⓘ	7.2992e-03
Maximal coefficientⓘ	4.7512e+01
Infeasibility of initial pointⓘ	13.36
Sparsity Jacobianⓘ
Sparsity 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.. -((0.156969560191053 + log(x4/(x4 + x7 + x10)))*x4 + (0.156969560191053 + 
     log(x7/(x4 + x7 + x10)))*x7 + (0.156969560191053 + log(x10/(x4 + x7 + x10)
     ))*x10 + log(3.9235*x2 + 6.0909*x5 + 0.92*x8)*(26.9071667605344*x2 + 
     41.7710875549227*x5 + 6.30931398488382*x8) + 0.113370955614741*x2 - 
     2.43897680885457*x5 + 2.8555953099828*x8 + 9.58716676053442*log(x2)*x2 + 
     16.9310875549227*log(x5)*x5 + 0.309313984883821*log(x8)*x8 - 
     9.58716676053442*log(3.9235*x2 + 6.0909*x5 + 0.92*x8)*x2 - 
     16.9310875549227*log(3.9235*x2 + 6.0909*x5 + 0.92*x8)*x5 - 
     0.309313984883821*log(3.9235*x2 + 6.0909*x5 + 0.92*x8)*x8 + 18.32*log(x2)*
     x2 + 25.84*log(x5)*x5 + 7*log(x8)*x8 - 18.32*log(3.664*x2 + 5.168*x5 + 1.4
     *x8)*x2 - 25.84*log(3.664*x2 + 5.168*x5 + 1.4*x8)*x5 - 7*log(3.664*x2 + 
     5.168*x5 + 1.4*x8)*x8 + log(4.0643*x2 + 5.7409*x5 + 1.6741*x8)*(4.0643*x2
      + 5.7409*x5 + 1.6741*x8) + 4.0643*log(x2)*x2 + 5.7409*log(x5)*x5 + 1.6741
     *log(x8)*x8 - 4.0643*log(4.0643*x2 + 3.22644664511275*x5 + 
     1.44980651607875*x8)*x2 - 5.7409*log(5.31147575751424*x2 + 5.7409*x5 + 
     0.00729924451284409*x8)*x5 - 1.6741*log(2.25846661774355*x2 + 
     3.70876916588753*x5 + 1.6741*x8)*x8 + log(3.9235*x3 + 6.0909*x6 + 0.92*x9)
     *(26.9071667605344*x3 + 41.7710875549227*x6 + 6.30931398488382*x9) + 
     0.113370955614741*x3 - 2.43897680885457*x6 + 2.8555953099828*x9 + 
     9.58716676053442*log(x3)*x3 + 16.9310875549227*log(x6)*x6 + 
     0.309313984883821*log(x9)*x9 - 9.58716676053442*log(3.9235*x3 + 6.0909*x6
      + 0.92*x9)*x3 - 16.9310875549227*log(3.9235*x3 + 6.0909*x6 + 0.92*x9)*x6
      - 0.309313984883821*log(3.9235*x3 + 6.0909*x6 + 0.92*x9)*x9 + 18.32*log(
     x3)*x3 + 25.84*log(x6)*x6 + 7*log(x9)*x9 - 18.32*log(3.664*x3 + 5.168*x6
      + 1.4*x9)*x3 - 25.84*log(3.664*x3 + 5.168*x6 + 1.4*x9)*x6 - 7*log(3.664*
     x3 + 5.168*x6 + 1.4*x9)*x9 + log(4.0643*x3 + 5.7409*x6 + 1.6741*x9)*(
     4.0643*x3 + 5.7409*x6 + 1.6741*x9) + 4.0643*log(x3)*x3 + 5.7409*log(x6)*x6
      + 1.6741*log(x9)*x9 - 4.0643*log(4.0643*x3 + 3.22644664511275*x6 + 
     1.44980651607875*x9)*x3 - 5.7409*log(5.31147575751424*x3 + 5.7409*x6 + 
     0.00729924451284409*x9)*x6 - 1.6741*log(2.25846661774355*x3 + 
     3.70876916588753*x6 + 1.6741*x9)*x9 - 0.3658348*x2 - 0.3658348*x3 - 
     0.9825555*x5 - 0.9825555*x6 - 0.3663657*x8 - 0.3663657*x9 - 
     30.9714667605344*log(x2)*x2 - 47.5119875549227*log(x5)*x5 - 
     7.98341398488382*log(x8)*x8 - 30.9714667605344*log(x3)*x3 - 
     47.5119875549227*log(x6)*x6 - 7.98341398488382*log(x9)*x9) + objvar =E= 0;

e2..    x2 + x3 + x4 =E= 40.30707;

e3..    x5 + x6 + x7 =E= 5.14979;

e4..    x8 + x9 + x10 =E= 54.54314;

* set non-default bounds
x2.lo = 1E-7; x2.up = 40.30707;
x3.lo = 1E-7; x3.up = 40.30707;
x4.lo = 1E-7; x4.up = 40.30707;
x5.lo = 1E-7; x5.up = 5.14979;
x6.lo = 1E-7; x6.up = 5.14979;
x7.lo = 1E-7; x7.up = 5.14979;
x8.lo = 1E-7; x8.up = 54.54314;
x9.lo = 1E-7; x9.up = 54.54314;
x10.lo = 1E-7; x10.up = 54.54314;

* set non-default levels
x2.l = 31.459;
x3.l = 0.901998;
x5.l = 3.10348;
x6.l = 9.6E-6;
x8.l = 26.1669;
x9.l = 15.0141;

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;