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.


Dr. Vera Roshchina

Research Area

RMIT University


Wed, 25/11/2015 - 2:05pm to 2:55pm


RC-M032, The Red Centre, UNSW