使用Python求函数最小值

现已知函数f(x) = (x0)**2 + (x1)**2，使用Python求其最小值。

import numpy as np
import matplotlib.pyplot as plt


def _numerical_gradient_no_batch(f, x):
    h = 1e-4
    grad = np.zeros_like(x)
    
    for idx in range(x.size):
        tmp_val = x[idx]
        x[idx] = tmp_val + h
        fxh1 = f(x)
        
        x[idx] = tmp_val - h
        fxh2 = f(x)
        
        grad = (fxh1 - fxh2) / (2*h)
        x[idx] = tmp_val
    
    return grad


def numerical_gradient(f, X):
    if X.ndim == 1:
        return _numerical_gradient_no_batch(f, X)
    else:
        grad = np.zeros_like(X)
        
        for idx, x in enumerate(X)：
            grad[idx] = _numerical_gradient_no_batch(f, x)
        
        return grad


def gradient_discent(f, init_x, lr=0.01, step_num=100):
    x = init_x
    x_history = []

    for i in range(step_num):
        x_history.append(x.copy())
        
        grad = numerical_gradient(f, x)
        x -= lr*grad
    
    return x, np.array(x_history)


def function_2(x):
    return x[0]**2 + x[1]**2


init_x = np.array([-3.0, 4.0])
lr = 0.1
step_num = 20
x, x_history = gradient_discent(function_2, init_x, lr=lr, step_num=step_num)

plt.plot([-5, 5], [0, 0], '--b')
plt.plot([0, 0], [-5, 5], '--b')
plt.plot(x_history[:, 0], x_history[:, 1], 'o')

plt.xlim(-3.5, 3.5)
plt.ylim(-4.5, 4.5)
plt.xlabel('x0')
plt.ylabel('x1')
plt.show()


        

print(x)
print(x_history)
print(x_history.shape)

[-0.03458765  0.04611686]
[[-3.          4.        ]
 [-2.4         3.2       ]
 [-1.92        2.56      ]
 [-1.536       2.048     ]
 [-1.2288      1.6384    ]
 [-0.98304     1.31072   ]
 [-0.786432    1.048576  ]
 [-0.6291456   0.8388608 ]
 [-0.50331648  0.67108864]
 [-0.40265318  0.53687091]
 [-0.32212255  0.42949673]
 [-0.25769804  0.34359738]
 [-0.20615843  0.27487791]
 [-0.16492674  0.21990233]
 [-0.1319414   0.17592186]
 [-0.10555312  0.14073749]
 [-0.08444249  0.11258999]
 [-0.06755399  0.09007199]
 [-0.0540432   0.07205759]
 [-0.04323456  0.05764608]]
(20, 2)