MILP using CVXPY

[Pravin Bezwada]

Hi,

I have the following method that tried to solve a linear problem and has constraints on the absolute value of weight. Since SOS1 constraints are not supported by CVXPY, I used binary variables (y) to recreate SOS1 constraints. The problem solves are returns status as 'optimal' but when I check the value of variable y which is defined as an Int, the values are 0.5. How is that possible? Please let me know if I missed something.

Best regards,

Pravin

import cvxpy as cvx

def getW(betas, signal, P):

    (m, n) = betas.shape

    x = cvx.Variable(4 * m)

    objective = cvx.Maximize(signal.T * x[2*m:-m])

    y = cvx.Int(2*m)

    

    constraints = [x[:m] >= 0, x[m:2*m] <= 0, P.T * x[2*m:-m] == 0, y <= 1, y >= 0]

    

    for i in range(0, n):

        constraints.append(betas[:, i].T * x[2*m:-m] == 0)

    

    for i in range(0, m):

        constraints.append(x[i] - x[m+i] - x[2*m+i] == 0)

        constraints.append(x[i] + x[m+i] - x[3*m+i] == 0)

        constraints.append(x[i] <= y[i])

        constraints.append(-x[m+i] <= y[m+i])

        constraints.append(y[i] + y[m+i] == 1)

        #constraints.append(P[i] * x[3*m+i] < 0.1 * P.T * x[-m:])

        

    prob = cvx.Problem(objective, constraints)

    prob.solve()

    print prob.status

    return np.squeeze(np.asarray(x.value[2*m:-m]))

[Steven Diamond]

I don't know why ``y`` wouldn't be an int after solve. I need a fully self-contained example script to say more about this problem.