Optimization (sampling) algorithms and (stochastic) differential equations: Theory and Insights (Konstantinos C. Zygalakis, Edinburgh)

27.01.2026 14:00

The ability of calculating the minimum (maximum) of a function lies in the heart of many applied mathematics applications. In this talk, we will connect such optimization problems to the large time behaviour of solutions to differential equations. We will then establish (a control theoretic) frame-work that allow us to deduce their long-time properties as well as deducing the long-time properties of their numerical discretisations. Using this framework, we give an alternative explanation for the good properties of Nesterov method for strongly convex functions, as well as highlight the reasons behind the failure of the heavy ball method. If there is time we will discuss how to generalise these ideas in a non-Euclidean setting as well as how to extend this framework to study the non-asymptotic behaviour of the numerical solutions of stochastic differential equations.

Lieu

Conseil Général 7-9, Room 8-02 (UNUSUAL ROOM!), Séminaire d'analyse numérique

entrée libre