从CVX到CVXPY或CVXOPT

Question

我一直在尝试将一些代码从Matlab传递到Python。我在Matlab上也有同样的凸优化问题，但是我在将它传递给CVXPY或CVXOPT时遇到了问题。

n = 1000;
i = 20;
y = rand(n,1);
A = rand(n,i);
cvx_begin
variable x(n);
variable lambda(i);
minimize(sum_square(x-y));
subject to
    x == A*lambda;
    lambda >= zeros(i,1);
    lambda'*ones(i,1) == 1;
cvx_end

这就是我用、Python、和CVXPY所做的尝试。

import numpy as np
from cvxpy import *

# Problem data.
n = 100
i = 20
np.random.seed(1)
y = np.random.randn(n)
A = np.random.randn(n, i)

# Construct the problem.
x = Variable(n)
lmbd = Variable(i)
objective = Minimize(sum_squares(x - y))
constraints = [x == np.dot(A, lmbd),
               lmbd <= np.zeros(itr),
               np.sum(lmbd) == 1]

prob = Problem(objective, constraints)

print("status:", prob.status)
print("optimal value", prob.value)

尽管如此，这是行不通的。你们中有谁知道怎么让它工作吗？我很确定我的问题是在约束中。还有，如果有CVXOPT的话，那就太好了。

Answer 1

我想我明白了，我有一个约束错误=)，我添加了一个随机的种子数，以便比较结果并检查在两种语言中实际上是相同的。我把数据留在这里，也许有一天这对某人有用;)

Matlab

rand('twister', 0);
n = 100;
i = 20;
y = rand(n,1);
A = rand(n,i);
cvx_begin
variable x(n);
variable lmbd(i);
minimize(sum_square(x-y));
subject to
    x == A*lmbd;
    lmbd >= zeros(i,1);
    lmbd'*ones(i,1) == 1;
cvx_end

CVXPY

import numpy as np
import cvxpy as cp

# random seed
np.random.seed(0)

# Problem data.
n = 100
i = 20
y = np.random.rand(n)
# A = np.random.rand(n, i)  # normal
A = np.random.rand(i, n).T  # in this order to test random numbers

# Construct the problem.
x = cp.Variable(n)
lmbd = cp.Variable(i)
objective = cp.Minimize(cp.sum_squares(x - y))
constraints = [x == A*lmbd,
               lmbd >= np.zeros(i),
               cp.sum(lmbd) == 1]

prob = cp.Problem(objective, constraints)
result = prob.solve(verbose=True)

CVXOPT正在等待.