1. function.py

   #coding:UTF-8
   '''
   Created on 2015年5月19日
   
   @author: zhaozhiyong
   '''
   
   from numpy import *
   
   #fun
   def fun(x):
       return 100 * (x[0,0] ** 2 - x[1,0]) ** 2 + (x[0,0] - 1) ** 2
   
   #gfun
   def gfun(x):
       result = zeros((2, 1))
       result[0, 0] = 400 * x[0,0] * (x[0,0] ** 2 - x[1,0]) + 2 * (x[0,0] - 1)
       result[1, 0] = -200 * (x[0,0] ** 2 - x[1,0])
       return result
   

   
   
2. 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
   

   
   
3. testDFP.py

   #coding:UTF-8
   '''
   Created on 2015年5月19日
   
   @author: zhaozhiyong
   '''
   
   from bfgs import *
   from dfp import dfp
   
   import matplotlib.pyplot as plt  
   
   x0 = mat([[-1.2], [1]])
   result = dfp(fun, gfun, x0)
   
   n = len(result)
   ax = plt.figure().add_subplot(111)
   x = arange(0, n, 1)
   y = result
   ax.plot(x,y)
   
   plt.show()
   

   
   

4、实验结果