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Instance ex7_3_6

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	inf (ANTIGONE) inf (BARON) inf (COUENNE) inf (LINDO) inf (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. Barmish, B R, New Tools for Robustness of Linear Systems, MacMillan Publishing Company, New York, NY, 1994. Abate, M, Barmish, B R, Murillo-Sanchez, C, and Tempo, R, Application of Some New Tools to Robust Stability Analysis of Spark Ignition Engines : A Case Study, IEEE Transactions on Control Systems Technology, 2:1, 1994, 22-30.
Sourceⓘ	Test Problem ex7.3.6 of Chapter 7 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	17
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	14
#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ⓘ	17
#Linear Constraintsⓘ	7
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	9
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	78
#Nonlinear Nonzeros in Jacobianⓘ	54
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	60
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	6
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	7
Maximal blocksize in Hessian of Lagrangianⓘ	7
Average blocksize in Hessian of Lagrangianⓘ	7.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.2899e-05
Maximal coefficientⓘ	9.0000e+00
Infeasibility of initial pointⓘ	3.433
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         18       11        0        7        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         18       18        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         80       26       54        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,objvar;

Positive Variables  x8,x9;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18;


e1..  - x9 + objvar =E= 0;

e2.. POWER(x8,4)*x14 - POWER(x8,6)*x16 - sqr(x8)*x12 + x10 =E= 0;

e3.. POWER(x8,6)*x17 - POWER(x8,4)*x15 + sqr(x8)*x13 - x11 =E= 0;

e4..  - x1 - 1.2721*x9 =L= -3.4329;

e5..  - x2 - 0.06*x9 =L= -0.1627;

e6..  - x3 - 0.0782*x9 =L= -0.1139;

e7..    x4 - 0.3068*x9 =L= 0.2539;

e8..  - x5 - 0.0108*x9 =L= -0.0208;

e9..    x6 - 2.4715*x9 =L= 2.0247;

e10..    x7 + 9*x9 =L= 1;

e11.. -(6.82079e-5*x1*x3*sqr(x4) + 6.82079e-5*x1*x2*x4*x5) + x10 =E= 0;

e12.. -(0.00076176*sqr(x2)*sqr(x5) + 0.00076176*sqr(x3)*sqr(x4) + 0.000402141*
      x1*x2*sqr(x5) + 0.00337606*x1*x3*sqr(x4) + 6.82079e-5*x1*x4*x5 + 
      0.00051612*sqr(x2)*x5*x6 + 0.00337606*x1*x2*x4*x5 + 6.82079e-5*x1*x2*x4*
      x7 + 6.28987e-5*x1*x2*x5*x6 + 0.000402141*x1*x3*x4*x5 + 6.28987e-5*x1*x3*
      x4*x6 + 0.00152352*x2*x3*x4*x5 + 0.00051612*x2*x3*x4*x6) + x11 =E= 0;

e13.. -(0.000402141*sqr(x5)*x1 + 0.00152352*sqr(x5)*x2 + 0.0552*sqr(x2)*sqr(x5)
       + 0.0552*sqr(x3)*sqr(x4) + 0.0189477*x1*x2*sqr(x5) + 0.034862*x1*x3*sqr(
      x4) + 0.00336706*x1*x4*x5 + 6.82079e-5*x1*x4*x7 + 6.28987e-5*x1*x5*x6 + 
      0.00152352*x3*x4*x5 + 0.00051612*x3*x4*x6 - 0.00234048*sqr(x3)*x4*x6 + 
      0.034862*x1*x2*x4*x5 + 0.0237398*sqr(x2)*x5*x6 + 0.00152352*sqr(x2)*x5*x7
       + 0.00051612*sqr(x2)*x6*x7 + 0.00336706*x1*x2*x4*x7 + 0.00287416*x1*x2*
      x5*x6 + 0.000804282*x1*x2*x5*x7 + 6.28987e-5*x1*x2*x6*x7 + 0.0189477*x1*
      x3*x4*x5 + 0.00287416*x1*x3*x4*x6 + 0.000402141*x1*x3*x4*x7 + 0.1104*x2*
      x3*x4*x5 + 0.0237398*x2*x3*x4*x6 + 0.00152352*x2*x3*x4*x7 - 0.00234048*x2
      *x3*x5*x6 + 0.00103224*x2*x5*x6) + x12 =E= 0;

e14.. -(0.189477*sqr(x5)*x1 + 0.1104*sqr(x5)*x2 + 0.00051612*x5*x6 + sqr(x2)*
      sqr(x5) + 0.00076176*sqr(x2)*sqr(x7) + sqr(x3)*sqr(x4) + 0.1586*x1*x2*
      sqr(x5) + 0.000402141*x1*x2*sqr(x7) + 0.0872*x1*x3*sqr(x4) + 0.034862*x1*
      x4*x5 + 0.00336706*x1*x4*x7 + 0.00287416*x1*x5*x6 + 6.28987e-5*x1*x6*x7
       + 0.00103224*x2*x6*x7 + 0.1104*x3*x4*x5 + 0.0237398*x3*x4*x6 + 
      0.00152352*x3*x4*x7 - 0.00234048*x3*x5*x6 + 0.1826*sqr(x2)*x5*x6 + 0.1104
      *sqr(x2)*x5*x7 + 0.0237398*sqr(x2)*x6*x7 - 0.0848*sqr(x3)*x4*x6 + 0.0872*
      x1*x2*x4*x5 + 0.034862*x1*x2*x4*x7 + 0.0215658*x1*x2*x5*x6 + 0.0378954*x1
      *x2*x5*x7 + 0.00287416*x1*x2*x6*x7 + 0.1586*x1*x3*x4*x5 + 0.0215658*x1*x3
      *x4*x6 + 0.0189477*x1*x3*x4*x7 + 2*x2*x3*x4*x5 + 0.1826*x2*x3*x4*x6 + 
      0.1104*x2*x3*x4*x7 - 0.0848*x2*x3*x5*x6 - 0.00234048*x2*x3*x6*x7 + 
      0.00076176*sqr(x5) + 0.0474795*x2*x5*x6 + 0.000804282*x1*x5*x7 + 
      0.00304704*x2*x5*x7) + x13 =E= 0;

e15.. -(0.1586*sqr(x5)*x1 + 0.000402141*sqr(x7)*x1 + 2*sqr(x5)*x2 + 0.00152352*
      sqr(x7)*x2 + 0.0237398*x5*x6 + 0.00152352*x5*x7 + 0.00051612*x6*x7 + 
      0.0552*sqr(x2)*sqr(x7) + 0.0189477*x1*x2*sqr(x7) + 0.0872*x1*x4*x5 + 
      0.034862*x1*x4*x7 + 0.0215658*x1*x5*x6 + 0.00287416*x1*x6*x7 + 0.0474795*
      x2*x6*x7 + 2*x3*x4*x5 + 0.1826*x3*x4*x6 + 0.1104*x3*x4*x7 - 0.0848*x3*x5*
      x6 - 0.00234048*x3*x6*x7 + 2*sqr(x2)*x5*x7 + 0.1826*sqr(x2)*x6*x7 + 
      0.0872*x1*x2*x4*x7 + 0.3172*x1*x2*x5*x7 + 0.0215658*x1*x2*x6*x7 + 0.1586*
      x1*x3*x4*x7 + 2*x2*x3*x4*x7 - 0.0848*x2*x3*x6*x7 + 0.0552*sqr(x5) + 
      0.3652*x2*x5*x6 + 0.0378954*x1*x5*x7 + 0.2208*x2*x5*x7) + x14 =E= 0;

e16.. -(0.0189477*sqr(x7)*x1 + 0.1104*sqr(x7)*x2 + 0.1826*x5*x6 + 0.1104*x5*x7
       + 0.0237398*x6*x7 + sqr(x2)*sqr(x7) + 0.1586*x1*x2*sqr(x7) + 0.0872*x1*
      x4*x7 + 0.0215658*x1*x6*x7 + 0.3652*x2*x6*x7 + 2*x3*x4*x7 - 0.0848*x3*x6*
      x7 + sqr(x5) + 0.00076176*sqr(x7) + 0.3172*x1*x5*x7 + 4*x2*x5*x7) + x15
       =E= 0;

e17.. -(0.1586*sqr(x7)*x1 + 2*sqr(x7)*x2 + 2*x5*x7 + 0.1826*x6*x7 + 0.0552*sqr(
      x7)) + x16 =E= 0;

e18.. -sqr(x7) + x17 =E= 0;

* set non-default bounds
x1.up = 3.4329;
x2.up = 0.1627;
x3.up = 0.1139;
x4.lo = 0.2539;
x5.up = 0.0208;
x6.lo = 2.0247;
x7.lo = 1;
x8.up = 10;
x9.up = 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;