拟牛顿法算法的设计与实现c语言,优化算法——拟牛顿法之DFP算法

dfp.py#coding:UTF-8

'''

Created on 2015年5月19日

@author: zhaozhiyong

'''

from numpy import *

from function import *

def dfp(fun, gfun, x0):

result = []

maxk = 500

rho = 0.55

sigma = 0.4

m = shape(x0)[0]

Hk = eye(m)

k = 0

while (k < maxk):

gk = mat(gfun(x0))#计算梯度

dk = -mat(Hk)*gk

m = 0

mk = 0

while (m < 20):

newf = fun(x0 + rho ** m * dk)

oldf = fun(x0)

if (newf < oldf + sigma * (rho ** m) * (gk.T * dk)[0,0]):

mk = m

break

m = m + 1

#DFP校正

x = x0 + rho ** mk * dk

sk = x - x0

yk = gfun(x) - gk

if (sk.T * yk > 0):

Hk = Hk - (Hk * yk * yk.T * Hk) / (yk.T * Hk * yk) + (sk * sk.T) / (sk.T * yk)

k = k + 1

x0 = x

result.append(fun(x0))

return result