## A Simple Derivation of a Facial Reduction Algorithm, and Extended Dual Systems

### Gabor Pataki

The Facial Reduction Algorithm (FRA) of Borwein and Wolkowicz, and the Extended Dual System (EDS) of Ramana aim to better understand duality, when a conic linear system $$Ax \leq_K b (P)$$ has no strictly feasible solution. We
• provide a simple proof of the correctness of a variant of FRA.
• show how it naturally leads to the validity of a family of extended dual systems.
• Summarize, which subsets of $K$ related to the system {P} (as the minimal cone and its dual) have an extended representation.

Technical Report, Dept. of IE/OR, Columbia University

Contact: gabor@ieor.columbia.edu