ValueError: установка элемента массива с последовательностью в функции минимизации CVXPY

Question

Я попытался решить выпуклую проблему с помощью cvxpy, как показано ниже.

        import cvxpy as cp
        import numpy as np

        # Problem data.
        Q = np.array([[13, 12, -2], [12, 17, 6], [-2, 6, 12]])
        q = np.array([[-22, -14.5, 13]])
        r = 1

        # Construct the problem.
        x = cp.Variable((3,1))
        objective = cp.Minimize(np.dot(np.dot(x.T, Q), x) + np.dot(q, x) + r)

        constraints = [0 <= x[0:], x[0:] <= 1]
        prob = cp.Problem(objective, constraints)

        # The optimal objective value is returned by `prob.solve()`.
        result = prob.solve()
        # The optimal value for x is stored in `x.value`.
        print(x.value)
        # The optimal Lagrange multiplier for a constraint is stored in
        # `constraint.dual_value`.
        print(constraints[0].dual_value)

Однако я получаю эту ошибку:

        ValueError: setting an array element with a sequence.

Я не знаю, почему эта ошибка возникает, потому что кажется, что все остальное работает.

Редактировать: Пожалуйста, дайте мне знать, если необходимо постановка задачи.

Answer 1

См. Комментарии выше:

import cvxpy as cp
import numpy as np

# Problem data.
Q = np.array([[13, 12, -2], [12, 17, 6], [-2, 6, 12]])
q = np.array([[-22, -14.5, 13]])
r = 1

# Construct the problem.
x = cp.Variable((3,1))

# WE CAN'T USE NUMPY'S DOT
# ALSO: WE WANT TO EXPRESS AS MUCH STRUCTURE AS POSSIBLE -> cp.quad_form()!
# q*x is cvxpy-compatible expression -> quite algebraic compared to numpy
# -------------------------------------------------------------------------
objective = cp.Minimize(cp.quad_form(x, Q) + q*x + r)

# ORIGINAL SLICING IS A NO-OP
# ---------------------------
constraints = [0 <= x, x <= 1]

prob = cp.Problem(objective, constraints)

        # The optimal objective value is returned by `prob.solve()`.
result = prob.solve()
        # The optimal value for x is stored in `x.value`.
print(x.value)
        # The optimal Lagrange multiplier for a constraint is stored in
        # `constraint.dual_value`.
print(constraints[0].dual_value)

Вывод:

[[ 8.46153846e-01]
[-6.34467676e-25]
[-1.92032635e-25]]
[[0.        ]
[5.80769231]
[9.61538462]]