梯度下降法求minf(x)=(x1-2)^4+(x1-2*x2)^2,其中，X=mat(x1,x2).T,选取初始点为X0= mat(0,3).T,终止误差为0.01

首先，求函数f(x)的偏导数：

∂f/∂x1 = 4(x1-2)^3(x1-2*x2) + 2(x1-2*x2)^2

∂f/∂x2 = -8(x1-2*x2)^2(x1-2)

然后，根据梯度下降法的公式，迭代更新X的值：

X(k+1) = X(k) - α∇f(X(k))

其中，α为学习率，可以根据实际情况调整。

代码如下：

import numpy as np

def f(x):
x1 = x[0]
x2 = x[1]
return (x1-2)**4 * (x1-2*x2)**2

def grad_f(x):
x1 = x[0]
x2 = x[1]
df_dx1 = 4*(x1-2)**3*(x1-2*x2) + 2*(x1-2*x2)**2
df_dx2 = -8*(x1-2*x2)**2*(x1-2)
return np.array([df_dx1, df_dx2])

def gradient_descent(X0, alpha, epsilon):
X = X0.copy()
while True:
grad = grad_f(X)
if np.linalg.norm(grad) < epsilon:
break
X = X - alpha*grad
return X

X0 = np.array([0, 3]).reshape(-1, 1)
alpha = 0.01
epsilon = 0.01
X = gradient_descent(X0, alpha, epsilon)
print(X)