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Removed Instance bearing

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
1.95173322 p1 ( gdx sol )
(infeas: 3e-14)
1.95168396 p2 ( gdx sol )
(infeas: 7e-10)
Other points (infeas > 1e-08)
1.93618060 p3 ( gdx sol )
(infeas: 5e-07)
1.92826666 p4 ( gdx sol )
(infeas: 9e-07)
1.91339147 p5 ( gdx sol )
(infeas: 9e-07)
Dual Bounds
1.95173322 (ANTIGONE)
1.90809929 (BARON)
1.86055753 (COUENNE)
1.95173322 (LINDO)
1.94733263 (SCIP)
References Siddall, James N, Optimal Engineering Design: Principles and Applications, Marcel Dekker, New York, 1982.
Deb, Kalyanmoy and Goyal, Mayank, Optimizing Engineering Designs Using a Combined Genetic Search. In Bäck, Thomas, Ed, Proceedings of the Seventh International Conference on Genetic Algorithms, 1997, 521-528.
Coello Coello, Carlos A, Treating Constraints as Objectives for Single-Objective Evolutionary Optimization, Engineering Optimization, 32:3, 2000, 275-308.
Source GAMS Model Library model bearing
Application Hydrostatic Thrust Bearing Design
Added to library 31 Jul 2001
Removed from library 16 Feb 2022
Removed because Difficult numerical behavior. Optimal value changes by > 2% when increasing feasibility tolerance.
Problem type NLP
#Variables 13
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 12
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 0
#Constraints 12
#Linear Constraints 3
#Quadratic Constraints 4
#Polynomial Constraints 3
#Signomial Constraints 0
#General Nonlinear Constraints 2
Operands in Gen. Nonlin. Functions log log10 vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 38
#Nonlinear Nonzeros in Jacobian 28
#Nonzeros in (Upper-Left) Hessian of Lagrangian 32
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 11
Average blocksize in Hessian of Lagrangian 6.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 6.0000e-06
Maximal coefficient 1.0965e+10
Infeasibility of initial point 1.008e+05
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
*         13       10        1        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         14       14        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         41       13       28        0
*
*  Solve m using NLP minimizing objvar;


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

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13;


e1..    10000*objvar - 10000*x7 - 10000*x8 =E= 0;

e2.. -1.42857142857143*x4*x6 + 10000*x8 =E= 0;

e3.. 10*x7*x9 - 0.00968946189201592*(x1**4 - x2**4)*x3 =E= 0;

e4.. 143.3076*x10*x4 - 10000*x7 =E= 0;

e5.. 3.1415927*(0.001*x9)**3*x6 - 6e-6*x3*x4*x13 =E= 0;

e6.. 101000*x12*x13 - 1.57079635*x6*x14 =E= 0;

e7.. log10(0.8 + 8.112*x3) - 10964781961.4318*x11**(-3.55) =E= 0;

e8..  - 0.5*x10 + x11 =E= 560;

e9..    x1 - x2 =G= 0;

e10.. 0.0307*sqr(x4) - 0.3864*sqr(0.0062831854*x1*x9)*x6 =L= 0;

e11..    101000*x12 - 15707.9635*x14 =L= 0;

e12.. -(log(x1) - log(x2)) + x13 =E= 0;

e13.. -(sqr(x1) - sqr(x2)) + x14 =E= 0;

* set non-default bounds
x1.lo = 1; x1.up = 16;
x2.lo = 1; x2.up = 16;
x3.lo = 1; x3.up = 16;
x4.lo = 1; x4.up = 16;
x6.lo = 1; x6.up = 1000;
x7.lo = 0.0001;
x8.lo = 0.0001;
x9.lo = 1;
x10.up = 50;
x11.lo = 100;
x12.lo = 1;
x13.lo = 0.0001;
x14.lo = 0.01;

* set non-default levels
x1.l = 6;
x2.l = 5;
x3.l = 6;
x4.l = 3;
x6.l = 1000;
x7.l = 1.6;
x8.l = 0.3;
x10.l = 50;
x11.l = 600;

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: 2022-04-26 Git hash: de668763
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