14h45: Francis Bach (Ecole Normale Supérieure Paris, INRIA, Lauréat 2019 du prix Jean Jacques Moreau):
Optimization at the heart of machine learning
Most machine learning methods are formulated as optimization problems. This has given rise to numerous exchanges between these two fields, with an increasing specialisation in the constraints of learning. In this presentation, I will illustrate these exchanges on non-smooth optimization for parsimony and stochastic gradient methods.
15h15: Giuseppe Buttazzo (Università di Pisa)
Relations between torsional rigidity and principal eigenvalue
The relations between principal eigenvalue of the Laplace operator in a domain with Dirichlet boundary conditions, and torsional rigidity, are studied in the class of general domains, convex domains, and domains with a small thickness. This is of help to provide some bounds for the Blaschke-Santalo diagram of the two quantities. This is an ongoing research with Michiel van den Berg (Bristol) and Aldo Pratelli (Pisa).
15h45: Bertrand Maury (Ecole Normale Supérieure Paris):
Sweeping process, optimal transport, and crowd movements
In a short note to the 1973 Comptes Rendus de l'Académie des Sciences, Jean-Jacques Moreau introduced the sweeping process of a point in a Hilbert space by a moving convex set. This pioneering work has generated a considerable amount of academic work since then, which generalizes the approach to all kinds of situations. We propose to describe some unexpected applications of this general framework to crowd movement modeling, which have recently led us to extend this sweeping process to the space of measures with the Wasserstein distance from optimal transport.
16h45: Vincent Acary (INRIA Grenoble)
Dynamics in finite dimension in the presence of unilateral contact, friction and impacts. The non-smooth approach.
In this paper, we will recall J.J. Moreau's fundamental contributions to the study of non-smooth dynamics for finite dimensional mechanical systems subjected to unilateral constraints, Coulomb friction and impacts. In particular, it will be shown how the formulation of Moreau's second-order sweeping process, in terms of differential measures, allows the design of robust and efficient numerical time integration methods. Recent results in this field will be discussed and illustrated on industrial applications.
