Some convex sets are particularly nice

Abstract

As the constraints of many continuous optimisation problems are represented by convex sets, and as we continue developing and improving sophisticated techniques for solving such problems, it is crucial to understand how irregularities in the facial structure affect the performance of numerical methods and to describe these irregularities in a constructive manner.

In this talk I will focus on the notion of amenability that appears to be well-suited for capturing good geometry of feasible sets, in particular in the framework of conic optimisation problems. I will show how this notion is related to other important properties, such as facial exposure, projective exposure and facial dual completeness, and will also introduce some open questions.

The talk is based on joint work with Dr Bruno Lourenço (The Institute of Statistical Mathematics, Japan) and Dr James Saunderson (Monash University), arXiv:2011.07745.

Short bio

Dr Vera Roshchina is a Senior Lecturer at the School of Mathematics and Statistics, UNSW Sydney. She works in convex geometry and optimisation, and has made research contributions to the areas of subdifferential calculus, geometry of convex sets, projection methods and mathematical billiards.

Vera is a recipient of the 2021 Christopher Heyde Medal from the Australian Academy of Science, and is currently holding two ARC Discovery grants. Prior to moving to UNSW Sydney in 2018 she was a DECRA Research Fellow at RMIT University and held postdoctoral positions at the University of Melbourne, Federation University and the University of Évora in Portugal.