Published Paper
Inserted: 18 may 2020
Last Updated: 11 apr 2021
Journal: J. Pure Appl. Algebra
Volume: 225
Number: 7
Year: 2021
Doi: doi.org/10.1016/j.jpaa.2020.106605
Abstract:
We revisit facial reduction from the point of view of projective geometry. This leads us to a homogenization strategy in conic programming that eliminates the phenomenon of weak infeasibility. For semidefinite programs (and others), this yields infeasibility certificates that can be checked in polynomial time. Furthermore, we propose a refined type of infeasibility, which we call stably infeasible, for which rational infeasibility certificates exist and that can be distinguished from other infeasibility types by our homogenization.