Can't find a solution that's not full-dimensional

[jtuckerfoltz]

Can't find a solution that's not full-dimensional

[stephane-caron]

Yes, compute_polytope_vertices won't work well with tight constraints such as the equality constraint you have formulated this way. If we relax the equality constraint a bit it will find a solution:

import pypoman
import numpy as np

# Original problem
A_1 = np.array([[-1, -1, -1], [1, 1, 1], [-1, 0, 0], [1, 0, 0], [0, -1, 0],
                [0, 1, 0], [0, 0, -1], [0, 0, 1], [1, 0, 0]])
b_1 = np.array([-1, 1, -0.0001, 0.4999, -0.0001, 0.4999, -0.0001, 0.4999,
                0.4999])
print("{} vertices".format(len(pypoman.compute_polytope_vertices(A_1, b_1))))

# Add new variable
A_2 = np.hstack([[[-1], [1], [0], [0], [0], [0], [0], [0], [1]], A_1])
b_2 = b_1

# Add (relaxed) constraint that new variable is == 0
epsilon = 1e-3
A_2 = np.vstack([A_2, [[-1, 0, 0, 0], [1, 0, 0, 0]]])
b_2 = np.hstack([b_2, epsilon, epsilon])
print("{} vertices".format(len(pypoman.compute_polytope_vertices(A_2, b_2))))

For me conversion of the second problem works down to epsilon = 1e-4, and starts to fail around epsilon = 1e-5.

For equality constraints, you could switch to pycddlib directly and use the linear set lin_set of equality-constraint generators. I'm not actively developing pypoman any more, but I'd be glad to merge a PR adding this feature to it as well 😉

[stephane-caron]

Closing this issue now, feel free to re-open for further discussion.