CVXPY constraint on 2d array with 3 elements referenced simultaneously

Question

I have a matrix S of size VxV. I want to impose several contraints on it of the form: . I have attempted to do so, but this code runs into the issue ValueError: Atoms must be at most 2D.

I put together a simplified example of my problem:

def ILP_example(scores):
    V = scores.shape[0]
    u, v, w = np.meshgrid(range(V), range(V), range(V))

    arr = cp.Variable(scores.shape)

    objective = cp.Maximize(
        cp.sum(cp.multiply(scores, arr))
    )
    constraints = [
        arr[u, v]           + arr[v, w]          - arr[u, w]          <= 1,
      ]
    prob = cp.Problem(objective, constraints)
    prob.solve()
    return

Attempting to run this, for example with ILP_example(np.random.rand(5, 5)) results in the error ValueError: Atoms must be at most 2D. How do I fix this?

Answer 1

It seems that cvxpy doesn't support more than 2 dimensions, which is what you are doing when you are indexing arr with u, v and w.

As an alternative you can simply reshape those indexing variables so they are 1 dimensional:

u, v, w = [x.reshape(-1) for x in np.meshgrid(range(V), range(V), range(V))]

Then this works just fine:

constraints = [arr[u, v] + arr[v, w] + arr[u, w] <= 1]

arr[u, v] is a 125 length vector now:

Expression(AFFINE, UNKNOWN, (125,))