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 上遇到了同样的凸优化问题，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

这是我用 Python 和 CVXPY.

尝试的结果

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，它不起作用。你们中有人知道如何让它发挥作用吗？我很确定我的问题出在 constraints 上。如果能和 CVXOPT 一起使用就好了。

Answer 1

我想我明白了，我有一个约束错误 =)，我添加了一个随机种子数以比较结果并检查两种语言中的结果是否相同。我把数据留在这里，所以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 待定.....

从 CVX 到 CVXPY 或 CVXOPT

From CVX to CVXPY or CVXOPT

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