Vera Roshchina (UNSW Sydney)
Performance of many numerical methods in convex optimisation is tied to the geometric properties of the objects that comprise the problem’s constraints. I am interested in extracting the mathematical description of specific features that affect the behaviour of convex objects and in constructing explicit examples that showcase these often counterintuitive properties. In this talk I would like to give an overview of some classical tools used in convex geometry, show some interesting examples of convex sets, and also talk about my recent work on amenable cones and hyperbolic programming. I will focus on motivation coming from applications and major open problems, and also on specific tools used in the proofs that will hopefully be of some interest to a broad audience.
The talk is based on collaborative work with Bruno Lourenço (The Institute of Statistical Mathematics, Japan) and James Saunderson (Monash University).
This is a hybrid seminar - it will be delivered face-to-face at UNSW and also livestreamed to an online audience.