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Instance ex14_2_4

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 9e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) -0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (LINDO) 0.00000000 (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.
Sourceⓘ	Test Problem ex14.2.4 of Chapter 14 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	7
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	6
Operands in Gen. Nonlin. Functionsⓘ	div mul sqr
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	33
#Nonlinear Nonzeros in Jacobianⓘ	24
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	9.1052e-02
Maximal coefficientⓘ	3.9849e+03
Infeasibility of initial pointⓘ	0.001683
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        2        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         35       11       24        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar,x6;

Positive Variables  x6;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1..    objvar - x6 =E= 0;

e2.. (0.549337520233386*x2 + 1.1263896788319*x3)/(x1 + 0.816722116903399*x2 + 
     0.538540530229217*x3) + 0.0910522583583458*x2/(0.972203312166101*x1 + x2
      + 0.394821041898112*x3) - 0.273994101407968*x3/(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3) - (x1*(0.549337520233386*x2 + 1.1263896788319*
     x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*x3) + 
     0.972203312166101*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
     0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 1.07810138009609*x3*(
     0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3)) - 3667.70490156687/(226.184 + x4) - x6
      =L= -12.0457123581059;

e3.. (0.0910522583583458*x1 + 1.03765878646318*x3)/(0.972203312166101*x1 + x2
      + 0.394821041898112*x3) + 0.549337520233386*x1/(x1 + 0.816722116903399*x2
      + 0.538540530229217*x3) + 0.692718766203089*x3/(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3) - (0.816722116903399*x1*(0.549337520233386*x2
      + 1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*
     x3) + x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
     0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 0.707289137797622*x3*(
     0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3)) - 2904.34268119711/(221.969 + x4) - x6
      =L= -9.63112952618865;

e4.. (0.692718766203089*x2 - 0.273994101407968*x1)/(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3) + 1.1263896788319*x1/(x1 + 0.816722116903399*x2
      + 0.538540530229217*x3) + 1.03765878646318*x2/(0.972203312166101*x1 + x2
      + 0.394821041898112*x3) - (0.538540530229217*x1*(0.549337520233386*x2 + 
     1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*x3)
      + 0.394821041898112*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
     0.972203312166101*x1 + x2 + 0.394821041898112*x3) + x3*(0.692718766203089*
     x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 0.707289137797622*x2
      + x3)) - 3984.92283948829/(233.426 + x4) - x6 =L= -11.9515596536534;

e5.. (-(0.549337520233386*x2 + 1.1263896788319*x3)/(x1 + 0.816722116903399*x2
      + 0.538540530229217*x3)) - (0.0910522583583458*x2/(0.972203312166101*x1
      + x2 + 0.394821041898112*x3) - 0.273994101407968*x3/(1.07810138009609*x1
      + 0.707289137797622*x2 + x3)) + x1*(0.549337520233386*x2 + 
     1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*x3)
      + 0.972203312166101*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
     0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 1.07810138009609*x3*(
     0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3) + 3667.70490156687/(226.184 + x4) - x6
      =L= 12.0457123581059;

e6.. (-(0.0910522583583458*x1 + 1.03765878646318*x3)/(0.972203312166101*x1 + x2
      + 0.394821041898112*x3)) - (0.549337520233386*x1/(x1 + 0.816722116903399*
     x2 + 0.538540530229217*x3) + 0.692718766203089*x3/(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3)) + 0.816722116903399*x1*(0.549337520233386*x2
      + 1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*
     x3) + x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
     0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 0.707289137797622*x3*(
     0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3) + 2904.34268119711/(221.969 + x4) - x6
      =L= 9.63112952618865;

e7.. (-(0.692718766203089*x2 - 0.273994101407968*x1)/(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3)) - (1.1263896788319*x1/(x1 + 0.816722116903399*
     x2 + 0.538540530229217*x3) + 1.03765878646318*x2/(0.972203312166101*x1 + 
     x2 + 0.394821041898112*x3)) + 0.538540530229217*x1*(0.549337520233386*x2
      + 1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*
     x3) + 0.394821041898112*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/
     sqr(0.972203312166101*x1 + x2 + 0.394821041898112*x3) + x3*(
     0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 
     0.707289137797622*x2 + x3) + 3984.92283948829/(233.426 + x4) - x6
      =L= 11.9515596536534;

e8..    x1 + x2 + x3 =E= 1;

* set non-default bounds
x1.lo = 1E-6; x1.up = 1;
x2.lo = 1E-6; x2.up = 1;
x3.lo = 1E-6; x3.up = 1;
x4.lo = 40; x4.up = 90;

* set non-default levels
x1.l = 0.187;
x2.l = 0.56;
x3.l = 0.253;
x4.l = 72.957;

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;