Cesare Molinari est Assistant Professor à l'Université de Gênes.
Titre : Gradient Flows and New Trends in Optimization
Résumé : The course presents gradient flows in Hilbert spaces – and subgradient flows in the nonsmooth case – as a unifying framework for designing and analyzing optimization algorithms. Participants will learn how to bridge continuous and discrete time, deriving classical first-order methods as discretizations of these evolution equations and studying their convergence, convergence rates and stability. The Kurdyka–Łojasiewicz (KL) property will play a central role, providing a unified perspective in both settings. The second part of the course covers recent trends that go beyond classical first-order methods: zeroth-order (derivative-free) proximal methods based on Hamilton–Jacobi equations, and consensus-based optimization, a particle method for global nonconvex optimization. Both are approached with the continuous-time and PDE tools developed in the first part.
Le cours est ouvert à tous et la participation est gratuite; néanmoins, pour des raisons d'organisation (salle, pauses café), nous demandons aux personnes intéressées de bien vouloir remplir ce très court formulaire.
Ce cours permet aux étudiants en thèse à l'EDMH de valider des heures de formation.