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Instance: ex7_3_4

Formats ams gms mod nl osil pip
Primal Bounds
10.00000000 p1 ( gdx sol )
(infeas: 0)
8.46047227 p2 ( gdx sol )
(infeas: 8e-10)
6.27463434 p3 ( gdx sol )
(infeas: 5e-13)
Dual Bounds
6.27463433 (ANTIGONE)
6.27463432 (BARON)
6.27463434 (COUENNE)
6.27463434 (LINDO)
6.27463384 (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.
Vicino, A, Tesi, A, and Milanese, M, Computation of Nonconservative Stability Perturbation Bounds for Systems with Nonlinearly Correlated Uncertainties, IEEE Transactions on Automatic Control, 35:7, 1990, 835-841.
Source Test Problem ex7.3.4 of Chapter 7 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 12
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 9
#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 10
#Quadratic Constraints 1
#Polynomial Constraints 6
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 51
#Nonlinear Nonzeros in Jacobian 23
#Nonzeros in (Upper-Left) Hessian of Lagrangian 25
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 4
Maximal blocksize in Hessian of Lagrangian 5
Average blocksize in Hessian of Lagrangian 4.5
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 10
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
*         18        8        0       10        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         13       13        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         53       30       23        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,objvar;

Positive Variables  x11;

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


e1..  - x12 + objvar =E= 0;

e2.. POWER(x11,4)*x10 - sqr(x11)*x8 + x6 =E= 0;

e3.. sqr(x11)*x9 - x7 =E= 0;

e4..  - x1 - x12 =L= -10;

e5..    x1 - x12 =L= 10;

e6..    x2 - 0.1*x12 =L= 1;

e7..  - x2 - 0.1*x12 =L= -1;

e8..  - x3 - 0.1*x12 =L= -1;

e9..    x3 - 0.1*x12 =L= 1;

e10..  - x4 - 0.01*x12 =L= -0.2;

e11..    x4 - 0.01*x12 =L= 0.2;

e12..  - x5 - 0.005*x12 =L= -0.05;

e13..    x5 - 0.005*x12 =L= 0.05;

e14.. -54.387*x3*x2 + x6 =E= 0;

e15.. -0.2*(1364.67*x3*x2 - 147.15*x4*x3*x2) + 5.544*x5 + x7 =E= 0;

e16.. -3*(-9.81*sqr(x2)*x3 - 9.81*x3*x1*x2 - 4.312*sqr(x3)*x2 + 264.896*x3*x2
       + x4*x5 - 9.274*x5) + x8 =E= 0;

e17.. -(7*sqr(x3)*x4*x2 - 64.918*sqr(x3)*x2 + 380.067*x3*x2 + 3*x5*x2 + 3*x5*x1
      ) + x9 =E= 0;

e18.. -sqr(x3)*x2*(7*x1 + 4*x2) + x10 =E= 0;

* set non-default bounds
x11.up = 10;

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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