我想用 CVXPY 解决熵最大化问题

Question

我正在使用 python，但 s.t. 有问题。部分和最后 2 行， 我不知道我做错了什么，我找不到任何类似的例子， 我将不胜感激任何帮助 。

import numpy as np
c = np.array([[3,11,18,22],
              [12,3,12,19],
              [15.5,13,5,7],
              [24,18,8,5]])
C=1200
O=[400,460,400,702]
D=[260,400,500,802]
L=4
K=4


import cvxpy as cp
x = cp.Variable((K, L), PSD=True)
obj = cp.Maximize(cp.sum(cp.entr(x)))
#error
constraints = [(for j=1 to L: cp.sum(x[:j])==O[j]), (for i =1 to L: cp.sum(x[:j])==D[i]), (cp.sum(cp.sum(c @x)) == C)]
prob = cp.Problem(obj, constraints)
opt_val = prob.solve(solver=cp.CVXOPT, verbose=True)

print("\nThe optimal value is:", prob.value)
print('\nThe optimal solution is:')
print(x.value)

Answer 1

我试图重写你的代码：

import cvxpy as cp
import numpy as np
c = np.array([[3,11,18,22],
              [12,3,12,19],
              [15.5,13,5,7],
              [24,18,8,5]])
C=1200
O=[400,460,400,702]
D=[260,400,500,802]
L=4
K=4



x = cp.Variable((K, L),pos=True)  #pos AS X is allowed to be zero in your last constraint
obj = cp.Maximize(cp.sum(cp.entr(x)))
#error
constraints=[]
for i in range (K): 
    constraints += [cp.sum(x,axis=0)==O[i]] #Assign all the sum of columns to be equal O
for j in range (L):              
    constraints += [cp.sum(x,axis=1)==D[j]]   #Assign all the sum of rows to be equal D
constraints+=   [ (cp.sum(cp.multiply(c,x)) == C)]   # The sum of dot product of the c,x matrix equal to C

prob = cp.Problem(obj, constraints)

prob.solve()
print("\nThe optimal value is:", prob.value)
print('\nThe optimal solution is:')
print(x.value)

不幸的是，它返回：
最佳值为：-inf
最优解是：
没有

我不确定您示例中的常量是否应该收敛为解决方案。不管怎样，我希望你能从这里拿走它。