Facial Structure of Convex Cones and Pataki Sandwich Theorem

Abstract: 

The facial structure of general closed convex cones can be very complex (often surprisingly so). I will talk about two notions that capture the regularity properties of facial arrangements: facial exposure and facial dual completeness, which are important for a range of theoretical results and algorithms (notably facial reduction algorithm for general cones). These two properties are equivalent in three dimensions, but in general facial dual completeness is a stronger property. Additional conditions sandwiched between facial exposure and facial dual completeness are known as Pataki sandwich theorem. I will talk about the sandwich theorem, introduce some new conditions and show illustrative four dimensional examples.

This is joint work with Prof, Levent Tuncel, University of Waterloo.