优化目标函数如下：

该函数有四个极小值点，值都为0

先对函数进行绘图


初始化起始点，再设置优化器，进行梯度下降优化

完整代码：

import torch
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def himmelblau(x):
    return (x[0]**2 + x[1] -11)**2 + (x[0] + x[1]**2 -7)**2

x = np.arange(-6, 6, 0.1)
y = np.arange(-6, 6, 0.1)
print('x, y range:', x.shape, y.shape)

X, Y = np.meshgrid(x, y)
print('X, Y maps:', X.shape, Y.shape)
Z = himmelblau([X, Y])

fig = plt.figure('himmelblau')
ax = fig.gca(projection = '3d')
ax.plot_surface(X, Y, Z)
ax.view_init(60, -30)
ax.set_xlabel('x')
ax.set_ylabel('y')
plt.show()

x = torch.tensor([0., 0.], requires_grad=True)
optimizer = torch.optim.Adam([x], lr=0.001)

for step in range(20001):
    pred = himmelblau(x)
    
    optimizer.zero_grad()
    pred.backward()
    optimizer.step()
    
    if step % 2000 == 0:
        print('step {}: x={}, fx={}'.format(step, x.tolist(), pred.item()))