Решение оптимизационных задач в SciPy

In [1]:

    

from scipy import optimize


    

In [2]:

    

def f(x):   # The rosenbrock function
    return .5*(1 - x[0])**2 + (x[1] - x[0]**2)**2
    
print f([1, 1])


    

    




0.0

In [3]:

    

result = optimize.brute(f, ((-5, 5), (-5, 5)))
print result


    

    




[ 0.99999324  1.00001283]

In [4]:

    

print optimize.differential_evolution(f, ((-5, 5), (-5, 5)))


    

    




    nfev: 1803
 success: True
     fun: 1.9180451127782141e-20
       x: array([ 1.,  1.])
 message: 'Optimization terminated successfully.'
     nit: 59

In [5]:

    

import numpy as np

def g(x):
        return np.array((-2*.5*(1 - x[0]) - 4*x[0]*(x[1] - x[0]**2), 2*(x[1] - x[0]**2)))


    

In [6]:

    

print optimize.check_grad(f, g, [2, 2])


    

    




2.38418579102e-07

In [7]:

    

print optimize.fmin_bfgs(f, [2, 2], fprime=g)


    

    




Optimization terminated successfully.
         Current function value: 0.000000
         Iterations: 16
         Function evaluations: 24
         Gradient evaluations: 24
[ 1.00000017  1.00000026]

In [8]:

    

print optimize.minimize(f, [2, 2])


    

    




   status: 0
  success: True
     njev: 24
     nfev: 96
 hess_inv: array([[ 0.98632031,  1.97824298],
       [ 1.97824298,  4.46512254]])
      fun: 9.536835216356594e-15
        x: array([ 1.00000007,  1.00000005])
  message: 'Optimization terminated successfully.'
      jac: array([  4.74151523e-07,  -1.53924328e-07])

In [9]:

    

print optimize.minimize(f, [2, 2], method='BFGS')


    

    




   status: 0
  success: True
     njev: 24
     nfev: 96
 hess_inv: array([[ 0.98632031,  1.97824298],
       [ 1.97824298,  4.46512254]])
      fun: 9.536835216356594e-15
        x: array([ 1.00000007,  1.00000005])
  message: 'Optimization terminated successfully.'
      jac: array([  4.74151523e-07,  -1.53924328e-07])

In [10]:

    

print optimize.minimize(f, [2, 2], method='Nelder-Mead')


    

    




  status: 0
    nfev: 91
 success: True
     fun: 1.2311995365407462e-10
       x: array([ 0.99998568,  0.99996682])
 message: 'Optimization terminated successfully.'
     nit: 46