IACM Colloquium
Speaker:
Konstantinos Zygalakis
Mathematics of Data Science, University of Edinburgh
Title:
Optimization algorithms and differential equations: Theory and Insights
Abstract:
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) framework 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.
Short Bio:
Konstantinos Zygalakis is a Professor in the Mathematics of Data Science at the University of Edinburgh. He received a 5-year Diploma in Applied Mathematics and Physics from the National Technical University of Athens in 2004, and his MSc and PhD from the University of Warwick in 2005 and 2008 respectively. Before Edinburgh he was a David Chrigton fellow at the University of Cambridge and held further postdoctoral positions at the University of Oxford and the Swiss Federal Institute of Technology, Lausanne as well as a lectureship in Applied Mathematics at the University of Southampton. His research spans a number of areas in the intersection of applied mathematics, numerical analysis, statistics and data science. In 2011, he was awarded a Leslie Fox Prize in Numerical Analysis (IMA UK) and he was a Fellow of the Alan Turing Institute between 2016 and 2021. He has co-authored over sixty research articles, as well as a graduate textbook in the Mathematics of Data Assimilation.
Time, Date & Location:
14:00, Thursday, April 3rd, 2025, Fotakis Room