Conic programming: Infeasibility certificates and projective geometry

We revisit facial reduction from the point of view projective geometry. This leads us to a homogenization strategy in conic programming that eliminates phenomenon weak infeasibility. For semidefinite programs (and others), this yields infeasibility certificates can be checked polynomial time. Furthermore, we propose refined type infeasibility, which call stably infeasible, for rational exist and distinguished other types by our homogenization.