Abstracts

Rodolphe Sepulchre (University of Cambridge)

Monotonicity, from circuit design to convex optimisation, and back

Maximal monotonicity is a backbone of large-scale convex optimisation. I will review the history of that concept, which originated from circuit theory, and discuss how we use this concept in our current research on spiking control systems.

Philippe Toint (University of Namur)

Some recent results in complexity analysis for nonconvex optimization (including high-order models and critical points)

We review some recently obtained results about the worst-case complexity of optimization algorithms for nonconvex problems. These results cover the standard cases where first and second-derivatives are used, but also the less frequent use of high-order derivatives. This therefore requires the discussion of what is meant by high-order critical points. We will also consider extensions to situations where the objective-function or derivative's values cannot be computed exactly. Finally, we will briefly outline some very recent progress in the OFFO context (objective-function free optimization), a framework whose importance has grown due to its ubiquitous use in deep learning methods.