Public Thesis Defense of Teodor ROTARU - ICTEAM
sst |
Exact Performance Analysis of Fundamental First-Order Optimization Methods
February 9th, 2026, 4:00pm - Aula Arenberg Castle (Room 01.07),Kasteelpark Arenberg 1, 3001 Heverlee (Leuven)
This thesis determines the exact worst-case convergence speeds for three fundamental optimization methods: gradient descent, proximal gradient descent, and Douglas–Rachford splitting. Unlike traditional analyses that rely on big-O notation, this work establishes precise, non-improvable bounds to reveal the true theoretical limits of these algorithms when applied to smooth, weakly convex functions.
By using transparent, analytical proofs, inspired from computer-generated ones, the research unifies the understanding of these methods across different curvature regimes. The results bridge the gap between convex and nonconvex settings, providing a rigorous definition of the performance boundaries for these essential tools in first-order optimization.
Jury members
Prof. François GLINEUR (UCLouvain), Supervisor
Prof. Panagiotis PATRINOS (KU Leuven), Supervisor
Prof.em. Adhémar BULTHEEL (KU Leuven), Chairperson
Prof. Aritra KONAR (KU Leuven), Secretary
Prof. Julien HENDRICKX (UCLouvain)
Prof. Nick VANNIEUWENHOVEN (KU Leuven)
Dr. Nelly PUSTELNIK (CNRS UMR 5672, ENS Lyon, France)
Dr. Adrien TAYLOR (INRIA ENS Paris, France)