Title: Minimising the number of faces of a class of polytopes

Speaker: David Yost (Federation University Australia)

Date and Time: Wed Dec 1, 17:00 AEST (Register here for remote connection via Zoom)

Abstract:

Polytopes are the natural domains of many optimisation problems. We consider a “higher order” optimisation problem, whose domain is a class of polytopes, asking what is the minimum number of faces (of a given dimension) for this class, and which polytopes are the minimisers. Generally we consider the class of d-dimensional polytopes with V vertices, for fixed V and d. The corresponding maximisation problem was solved decades ago, but serious progress on the minimisation question has only been made in recent years auxiliary information will be provided.

Title: A Newton-MR Algorithm with Complexity Guarantee for Non-Convex Problemsverting exhausters and coexhausters

Speaker: Fred Roosta-Khorasani (The University of Queensland)

Date and Time: Wed Dec 1, 11:00 AEST (Register here for remote connection via Zoom)

Abstract:

Classically, the conjugate gradient (CG) method has been the dominant solver in most inexact Newton-type methods for unconstrained optimization. In this talk, we consider replacing CG with the minimum residual method (MINRES), which is often used for symmetric but possibly indefinite linear systems. We show that MINRES has an inherent ability to detect negative-curvature directions. Equipped with this advantage, we discuss algorithms, under the general name of Newton-MR, which can be used for optimization of general non-convex objectives, and that come with favourable complexity guarantees. We also give numerical examples demonstrating the performance of these methods for large-scale non-convex machine learning problems.