1、Rosenbrock函式

#！／user/bin/env python
#-*- coding:utf-8 -*-
#梯度下降Rosenbrock函式

def rb(x,y):
    #定義rosenbrock函式
    return (1-x)**2+100*(y-x**2)**2

def partial_x(x,y):
    #計算x的偏導數
    return -2*(1-x)-400*x*(y-x**2)

def partial_y(x,y):
    #計算y的偏導數
    return 200*(y-x**2)

def bgd_rosenbrock():
    x=0
 

    y=0
    i=0
    learning_rate = 0.001
    while i < 10000:
    #步長0.001下降10000步
        x = x - learning_rate * partial_x(x, y)
        y = y - learning_rate * partial_y(x, y)
        print('min',rb(x,y))
        i = i+1
bgd_rosenbrock()

最終最小結果

min 7.6209387766275974e-06