Can ECOS handle infinite values in inequality vectors?

[stephane-caron]

ECOS does not seem to handle infinite values in inequality bounds, which happen for instance when disabling an inequality while working on a problem (e.g. in box inequalities lb <= x <= ub). Right now the solver fails at first iteration if we put an infinite float (numpy.inf) in the inequality vector.

Reproduction steps

Here is an example:

import numpy as np
import scipy.sparse as spa
import ecos

c = np.array([0.0, 0.0, 1.0])
G = spa.csc_matrix(
    np.array(
        [
            [-1.0, 0.0, 0.0],
            [0.0, -1.0, 0.0],
            [1.0, 0.0, 0.0],
            [0.0, 1.0, 0.0],
            [0.0, 0.0, -0.70710678],
            [-1.0, 0.0, 0.0],
            [0.0, -1.0, 0.0],
            [0.0, 0.0, 0.70710678],
        ]
    )
)
h = np.array([1.0, np.inf, np.inf, 1.0, 0.70710678, 0.0, 0.0, 0.70710678])
dims = {"q": [4], "l": 4}
ecos.solve(c, G, h, dims)

It produces the following output:

ECOS 2.0.10 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS

It     pcost       dcost      gap   pres   dres    k/t    mu     step   sigma     IR    |   BT
 0   -nan   -inf  +nan  0e+00  7e-02  1e+00  nan    ---    ---    0  1  - |  -  - 
Reached NAN dead end, recovering best iterate (368424832) and stopping.

Close to OPTIMAL (within feastol=6.9e-310, reltol=6.9e-310, abstol=6.9e-310).
Runtime: 0.000546 seconds.

See also

This example was produced from a small 2D quadratic program with box inequalities qpsolvers/qpsolvers#160:

import numpy as np
from qpsolvers import solve_qp

# minimize 1/2 x^T P x + q^T x
P = np.eye(2)
q = np.zeros(2)

# subject to lb <= x <= ub
lb = np.array([-1.0, -np.inf])
ub = np.array([np.inf, 1.0])

solve_qp(P, q, lb=lb, ub=ub, solver="ecos")