CVXPY：如何最大化两个向量的点积

Question

假设我们有三个特征，每个特征有 252 个样本。 在这里，特征是三种不同股票的回报。 目标是最大化总回报，即

我的问题是如何在CVXpy优化问题中定义这个目标 function ？

程序的过程视图应如下所示：

import numpy as np
import cvxpy as cvx;

return1 = np.random.normal(loc=0.05, scale=0.25, size=252)
return2 = np.random.normal(loc=0.01, scale=0.2, size=252)
return3 = np.random.normal(loc= -0.05, scale=0.15, size=252)
returns = np.array([return1, return2, return3])

# number of stocks m is number of rows of returns
m = returns.shape[0]

# x variables (to be found with optimization)
x = cvx.Variable(m)

# portfolio return
portfolio_return = cvx.multiply(returns, x)

#objective function
objective = cvx.Minimize(-portfolio_return)

#constraints
constraints = [x >= 0, sum(x) == 1]

#use cvxpy to solve the objective
cvx.Problem(objective, constraints).solve()

#retrieve the weights of the optimized portfolio
x_values = x.value

print(x_values)

但是，它返回一个错误：

ValueError: Cannot broadcast dimensions  (3, 252) (3,)

当我们将 x 表示为x = cvx.Variable(shape=(m,1))我们得到另一个错误

ValueError: The 'minimize' objective must resolve to a scalar.

Python 版本：3.8.8

CVXPY 版本：1.1.12

Answer 1

感谢 cvxpy 社区，我重新表述了这个问题，现在它运行没有错误。

import numpy as np
import cvxpy as cvx;
return1 = np.random.normal(loc=0.05, scale=0.25, size=252)
return2 = np.random.normal(loc=0.01, scale=0.2, size=252)
return3 = np.random.normal(loc= -0.05, scale=0.15, size=252)
returns = np.array([return1, return2, return3])
m = returns.shape[0]
cov = np.cov(returns)
x = cvx.Variable(m)
portfolio_return = returns.mean(axis=1)
objective = cvx.Maximize(x @ portfolio_return)
constraints = [x >= 0, sum(x) == 1]
cvx.Problem(objective, constraints).solve()
x_values = x.value
x_values.round(2)