计算科学 - 关于 CVXPY 求解器的奇怪输出的问题 - 吾爱随笔录

我正在熟悉 CVXPY，遇到了一个奇怪的问题。我有以下简单的玩具优化问题：

import numpy as np
import cvxpy as cp

A=np.array([[1,0,0],[0,1,0], [0,0,1]])
y=np.array([1,1,1])

# Upper bound for the constraint term
upper=1
# Solve the optimization problem using CVXPY
x = cp.Variable(3)
objective = cp.Minimize(cp.sum_squares(x))
constraint = [cp.sum_squares(A*x - y) <= upper]
prob = cp.Problem(objective, constraint)
prob.solve()
optimal_x = x.value

print('Value of constraint at optimal x:' + str(np.linalg.norm(A*optimal_x - y)**2))

现在，我希望我的输出数比 samller 小upper=1，但我得到的是以下内容：

Value of constraint at optimal x:3.0000000068183947

我很困惑这怎么可能是真的。我是否cp.sum_squares错误地使用了该功能？我只是以错误的方式设置优化吗？任何帮助表示赞赏！

#!/usr/bin/env python3 import numpy as np import cvxpy as cp A=np.array([[1,0,0],[0,1,0], [0,0,1]]) y=np.array([1,1,1]) # Upper bound for the constraint term upper=1 # Solve the optimization problem using CVXPY x = cp.Variable(3) objective = cp.Minimize(cp.sum_squares(x)) constraint = [cp.sum_squares(A@x - y) <= upper] prob = cp.Problem(objective, constraint) prob.solve() optimal_x = x.value print('Value of constraint at optimal x: {0}'.format(np.linalg.norm(A@optimal_x - y)**2))