SCS fails to find solution under infinite linear bounds

[stephane-caron]

Converting disabled box bounds (i.e. coordinates at $-\infty$ for a lower or $+\infty$ for an upper bound) using the internal linear_from_box_inequalities function will result in new linear inequalities $G', h'$ where some values in $h'$ can be $\pm\infty$.

The qpSWIFT interface, for instance, does not handle this correctly, with the solver returning None (no solution) for problems that have solutions.

Reproduction steps

Here is an example reproducing this issue:

import numpy as np

from qpsolvers import solve_qp

M = np.array([[1.0, 2.0, 0.0], [-8.0, 3.0, 2.0], [0.0, 1.0, 1.0]])
P = np.dot(M.T, M)  # this is a positive definite matrix
q = np.dot(np.array([3.0, 2.0, 3.0]), M)
G = np.array([[4.0, 2.0, 0.0], [-1.0, 2.0, -1.0]])
h = np.array([np.inf, -2.0])
A = np.array([1.0, 1.0, 1.0]).reshape((1, 3))
b = np.array([1.0])
lb = np.array([-0.5, -0.4, -0.5])
ub = np.array([1.0, 1.0, 1.0])

x_cvx = solve_qp(P, q, G, h, lb=lb, ub=ub, solver="cvxopt")
print(f"CVXOPT solution: {x_cvx}")

x_scs = solve_qp(P, q, G, h, lb=lb, ub=ub, solver="scs")
print(f"SCSsolution: {x_scs}")

Outcome:

python bug_scs.py                                                                                                                       ✔  38s 
CVXOPT solution: [ 0.32941177 -0.4         0.87058824]
/home/nelson/src/qpsolvers/qpsolvers/conversions/warnings.py:35: UserWarning: Converted P to scipy.sparse.csc.csc_matrix
For best performance, build P as a scipy.sparse.csc_matrix rather than as a numpy.ndarray
  warnings.warn(
/home/nelson/src/qpsolvers/qpsolvers/conversions/warnings.py:35: UserWarning: Converted G to scipy.sparse.csc.csc_matrix
For best performance, build G as a scipy.sparse.csc_matrix rather than as a numpy.ndarray
  warnings.warn(
/home/nelson/src/qpsolvers/qpsolvers/solvers/scs_.py:246: UserWarning: SCS returned -6: UNBOUNDED_INACCURATE
  warnings.warn(
SCSsolution: None