An infeasible problem

[kkzhang3]

Hello! I try to test proxqp to solve an obvious infeasible problem.
I didn't get a clear infeasible result. I'm not sure if it is correct or not.
I was using proxsuite 0.6.5 with python 3.12.2 on windows 11 platform.
The code is as follow:

from scipy import sparse
import numpy as np
import proxsuite
print(f"{proxsuite.__version__ = }")
# (x1- 9)^2 + (x2-6)^2
# s.t.
# x1 <= 10
# x2 <= 10
# x1 >= 20
P = 2*sparse.csc_matrix([[1.0, 0.0], 
                         [0.0, 1.0]], dtype=float)
q = np.array([-18.0, 
              -12.0], dtype=float)
G = sparse.csc_matrix([[1,  0],  # x1 <= 10
                       [0,  1],  # x2 <= 10 
                       [-1, 0],  # x1 >= 20
                       ], dtype=float)
u = np.array([10, 
              10,
              -20,
              ], dtype=float)
n = P.shape[0]
n_in = G.shape[0]
n_eq = 0
A = None
b = None
l = np.full(n_in, -np.inf, dtype=float)
qp = proxsuite.proxqp.sparse.QP(n, n_eq, n_in)
qp.init(P, q, A, b, G, l, u)
solver_options = {"verbose": False, "max_iter": 3000}
for key, value in solver_options.items():
    setattr(qp.settings, key, value)
qp.solve()

print(f"PROXQP status: {qp.results.info.status.name}")
print(f"x: {qp.results.x}")
print(f"y: {qp.results.y}")
print(f"z: {qp.results.z}")
print(f"si: {qp.results.si}")
print(f"pri_res: {qp.results.info.pri_res}")
print(f"dua_res: {qp.results.info.dua_res}")
print(f"duality_gap: {qp.results.info.duality_gap}")

Results:

proxsuite.__version__ = '0.6.5'
PROXQP status: PROXQP_MAX_ITER_REACHED
x: [14.99999973  6.        ]
y: []
z: [0. 0. 0.]
si: [0. 0. 0.]
pri_res: 0.0
dua_res: 0.0
duality_gap: 179.99998851439864

[fabinsch]

Hi @kkzhang3, in the settings we have an option called check_duality_gap, which is set to False by default. If you turn it on, it should return PROXQP_PRIMAL_INFEASIBILITY in my opinion.

[kkzhang3]

I tried. It still returns PROXQP_MAX_ITER_REACHED. 'pri_res', 'dua_res' and 'si' are all zeros.

[kkzhang3]

I also found that the QP object status changed from PROXQP_NOT_RUN to PROXQP_MAX_ITER_REACHED after init (before solve). Is that normal?

[fabinsch]

Hi @kkzhang3 , we fixed the problem that you encountered in #328. I added the example above as unittest and it correctly returns PROXQP_PRIMAL_INFEASIBLE.

As soon as the PR is merged, we'll do a new release and you can easily install it via conda or pip. Otherwise, you can just pull the changes from the PR and build from source.

[kkzhang3]

Thanks!

[jcarpent]

A release is in the pipe.