CVXPY：约束冲突

Question

我试图在cvxpy中解决一个优化程序。问题在于它返回的答案违反了它所给出的基本约束。我以前成功地运行过这个程序，并试图模拟与以前相同的代码，但这个问题让我困惑了哪里出了问题。任何帮助都将不胜感激

我试图解决的优化问题：

obj funct: maximize 0.1a1 + 0.1428a2 + 0.2a3
s.t 7a1 + 11a2 + 16a3 <= 80
a1, a2, a3 > =0, all integers

当我运行下面的代码时，a1、a2和a3的值为5，这违反了给定的约束

import cvxpy as cvx
import numpy as np
import scipy as sc
from scipy import linalg

#Define Starting Matrix
A1 = np.array([10,0,0])
A2 = np.array([0,7,0])
A3 = np.array([0,0,5])

#Optimal Basis and Inverse
B = np.array([A1, A2, A3])
print(f"B:{B}")
Binv = linalg.inv(B)
print(f"B-1:{Binv}")

#Define Cost Matrix
c = np.array([1, 1, 1])

#Optimal Dual Solution, y.hat
yhat = np.matmul(c,Binv)
print(f"y.hat:{yhat}")

#Pricing Problem
a = cvx.Variable(shape=(3,1), name="a")
w = np.array([[7,11,16]])

#Define Obj Function
objective2 = cvx.Maximize(cvx.matmul(yhat,a))

#Define Constraints
constraint2 = [
    cvx.matmul(a,w)<=80,
    a >=0
]

#Define Problem and Solve
knapsack = cvx.Problem(objective2, constraint2)
solution2 = knapsack.solve()
print(solution2)
print(a.value)

---

2.2142857137502494    
[[5.]    
 [5.]    
 [5.]]

Answer 1

你的维度被打破了

与以下各项的矩阵乘法：

a = cvx.Variable(shape=(3,1), name="a")  # 3 x 1
w = np.array([[7,11,16]])                # 1 x 3

结果：

z = a * w      # 3 x 3

您可以轻松验证这一点：

print(cvx.matmul(a,w).shape)
# (3, 3)

您可能需要将列向量a更改为行向量a。这也意味着对w（以及我不想提及的其他表达式）进行转置：

a = cvx.Variable(shape=(1,3), name="a")
w = np.array([7,11,16]]).transpose()