cvxpy中的余数运算

Question

cvxpy 中是否有任何内置函数来计算变量的余数？例如下面的示例代码：

m = 3
n = 2
k = 5
A = cp.Variable((m,n),boolean=True)
B = np.ones((1,m))
C = np.ones(n)
constraints = []
objective = cp.Maximize((B@A%2)@C)
prob = cp.Problem(objective, constraints)
optimal_value = prob.solve()

给出错误：

Exception has occurred: TypeError
unsupported operand type(s) for %: 'MulExpression' and 'int'

因为%操作

Answer 1

余数r = a mod n，加上a ≥ 0，可得：

  a = q*n + r      (assume n is constant) 
  q ∈ {0,1,...}    (integer variable, non-negative}
  r ∈ {0,..,n-1}   (integer variable between 0 and n-1)

这只是一个线性约束。另见：https://en.wikipedia.org/wiki/Modulo_operation.

cvxpy中的余数运算

Remainder operation in cvxpy

python

python-3.x

optimization

cvxpy

convex-optimization