Python implements the steepest descent method
The examples in this article share the specific code of python to achieve the fastest descent method for your reference. The specific content is as follows
Code:
from sympy import*import numpy as np
def backtracking_line_search(f,df,x,x_k,p_k,alpha0):
rho=0.5
c=10**-4
alpha=alpha0
replacements1=zip(x,x_k)
replacements2=zip(x,x_k+alpha*p_k)
f_k=f.subs(replacements1)
df_p=np.dot([df_.subs(replacements1)for df_ in df],p_k)while f.subs(replacements2) f_k+c*alpha*df_p:
alpha=rho*alpha
replacements2 =zip(x, x_k +alpha * p_k)return alpha
def stepest_line_search(f,x,x0,alpha0):
df =[diff(f, x_)for x_ in x]
x_k=x0
alpha=alpha0
replacements=zip(x,x_k)
len_df =sqrt(np.sum([df_.subs(replacements)**2for df_ in df]))while len_df 1e-6:
p_k=-1*np.array([df_.subs(replacements)for df_ in df])
alpha =backtracking_line_search(f, df, x, x_k, p_k, alpha)
x_k=x_k+alpha*p_k
replacements =zip(x, x_k)
len_df=np.sum([df_.subs(replacements)**2for df_ in df])return x_k
if __name__=="__main__":init_printing(use_unicode=True)
x1 =symbols("x1")
x2 =symbols("x2")
x = np.array([x1, x2])
f =100*(x2 - x1 **2)**2+(1- x1)**2
ans=stepest_line_search(f, x, np.array([1.2,1]),1)
print "the minimal value in point:",ans
analysis:
This uses backtracking line search to find alpha.
The above is the whole content of this article, I hope it will be helpful to everyone's study.
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