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Instance: bearing

Formats ams gms mod nl osil
Primal Bounds
1.95173322 p1 ( gdx sol )
(infeas: 3e-14)
Dual Bounds
1.95173322 (ANTIGONE)
1.09632256 (BARON)
1.86055753 (COUENNE)
1.95173322 (LINDO)
1.94682655 (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
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 vcpower log10 log
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
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: 2018-09-14 Git hash: ac5a5314
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