集合中的CVXPY等式約束

Question

我有一個ILP問題，我需要將變量矩陣的值約束在{0，1}中。 我嘗試使用以下（簡化）代碼執行此操作，但它不允許我使用“|” 運營商。 我該怎么做？

def test_ILP(scores):
    N = scores.shape[0]
    eye_bool = np.eye(N)
    zero_when_equal = np.abs(np.eye(N) - 1)


    opt = cp.Variable(scores.shape)
    objective = cp.Maximize(
        cp.sum(cp.multiply(scores, opt * zero_when_equal))
    )


    constraints = [(opt == 0) | (opt == 1) | eye_bool]

    prob = cp.Problem(objective, constraints)
    prob.solve()
    return opt.value

Answer 1

根據@ sascha的注釋，對於布爾（或整數）約束，可以使用Variable構造函數中的參數。 對於這種情況：

def test_ILP(scores):
    N = scores.shape[0]
    eye_bool = np.eye(N)
    zero_when_equal = np.abs(np.eye(N) - 1)
    boolean_constraint = [(x, y) for x in range(N) for y in range(N) if x != y]

    opt = cp.Variable(scores.shape, boolean=boolean_constraint)
    objective = cp.Maximize(
        cp.sum(cp.multiply(scores, opt * zero_when_equal))
    )


    constraints = [#Rest of the constraints]

    prob = cp.Problem(objective, constraints)
    prob.solve()
    return opt.value