Dynamics Seminar

Event Information Facial geometry of convex sets
13:10 on Friday March 09, 2018
14:00 on Friday March 09, 2018
BA2179, Bahen Center, 40 St. George St.
Vera Roshchina

RMIT University and Federation University Australia

Faces of convex sets generalise the notion of faces of polytopes (such as vertices, edges and facets). Many structural properties of convex sets can be expressed via faces and their arrangements. In particular, some regularity conditions that guarantee good performance of optimisation methods can be expressed in terms of facial structure.

I will mention some classical and recent results related to the facial structure of convex sets, and will illustrate the impact of facial structure on the performance of numerical methods using the recent counter-example to De Pierro's conjecture about the convergence of under-related cyclic projections.