Przykład 6.8. Rozwiązywanie zadanie optymalizacji

from biz.sc.math.opt import * 
from biz.sc.math.opt.alg import * 
from biz.sc.math.opt.nlf import *   
from biz.sc.math.opt.constraint import * 

from java.util import ArrayList 
from java.lang import System 

from biz.sc.math.opt.nlf import * 

class TestFunction(AbstractNLF): 
    def __init__(self, dim, type): 
        AbstractNLF.__init__(self, dim, type) 
        print "Function dimension : ", dim 
        print "Function type : ", type 

    def evaluate(self, x, fx, gx, Hx): 
        "@sig void evaluate(double[] x, double[] fx, double[] gx, double[][] Hx)" 
        
        if (fx != None): 
            fx[0] = x[0]*x[0]+x[1]*x[1]-2*x[1] 
        
        if (gx != None): 
            gx[0] = 2*x[0] 
            gx[1] = 2*x[1]-2 
        
        if (Hx != None): 
            Hx[0][0] = Hx[1][1] = 2 
            Hx[0][1] = Hx[1][0] = 0 


constr = ArrayList()

bounds = BoundConstraint([1, .5],[2,1]) 

constr.add(bounds)

optMethod = BCNewtonMethod() 

f = TestFunction(2, NLF.NLF2) 
f.setInitVector([1.3,0.6]) 

opt = Optimizer(f, optMethod, constr) 
opt.setMinimize();
opt.setOutput(sys.stdout, FALSE) # optimization information on standard output, false means without debug data 

res = opt.optimize() 

print res

Wynik:

Function dimension :  2
Function type :  2
**********************************************************
OPT++ version 2.1
Job run at Tue Sep 19 15:04:22 2006

**********************************************************
readOptInput: No opt.input file found
readOptInput: default values will be used


=========  Initial state  ===========


    i	    xc 		 grad 		 fcn_accrcy 
     1         1.3	         2.6	    2.22e-16
     2         0.6	        -0.8	    2.22e-16
Function Value     =         0.85
Norm of gradient   =         2.72


==============================================


                Bound constrained Newton Method with Line Search

  Iter      F(x)       ||grad||     ||step||      f/g

    0         0.85         2.72
    1      0.09467        2.093       0.3139  N     2     2
OptBCNewton : variable added to working set : 1
OptBCNewton: Current working set  
 ----- variable index:      1	1
     2            0            2       0.3077  N     3     3
checkConvg: gnorm =            0  gtol =    6.055e-06
OptBCNewton : variable added to working set : 2
OptBCNewton : reduced_grad_norm = 0
OptBCNewton: Current working set  
 ----- variable index:      1	1     2	1
 OptBCNewtonLike : convergence achieved. 


=========  Final state  ===========

Optimization method       = Bound constrained Newton
Dimension of the problem  = 2
No. of bound constraints  = 2
Return code               = 4 (Gradient tolerance test passed)
No. iterations taken      = 2
No. function evaluations  = 3
No. gradient evaluations  = 3


==========  Tolerances  ===========

Machine Epsilon      = 2.22045e-16
Maximum Step         = 1000
Minimum Step         = 1.49012e-08
Maximum Iter         = 100
Maximum Backtracks   = 5
Maximum Fcn Eval     = 1000
Step Tolerance       = 1.49012e-08
Function Tolerance   = 1.49012e-08
Constraint Tolerance = 1.49012e-08
Gradient Tolerance   = 6.05545e-06
LineSearch Tolerance = 0.0001


=========  Final state  ===========


    i	    xc 		 grad 		 fcn_accrcy 
     1           1	           2	    2.22e-16
     2           1	           0	    2.22e-16
Function Value     =            0
Norm of gradient   =            2


==============================================

array([1.0, 1.0], double)