Facial Structure of Convex Cones and Pataki Sandwich Theorem

Speaker: 

Dr. Vera Roshchina

Affiliation: 

RMIT University

Date: 

Wed, 25/11/2015 - 2:05pm to 2:55pm

Venue: 

RC-M032, The Red Centre, UNSW

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.

School Seminar Series: