Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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S. Naldi - R. Sinn

Conic programming: infeasibility certificates and projective geometry

created by naldi on 18 May 2020
modified on 11 Apr 2021


Published Paper

Inserted: 18 may 2020
Last Updated: 11 apr 2021

Journal: J. Pure Appl. Algebra
Volume: 225
Number: 7
Year: 2021

ArXiv: 1810.11792 PDF
Links: Publisher page


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.

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