13h40–14h00 — Salle du conseil (L2S)
Aggregative nonconvex optimization: two dual-based methods
Abstract. Problems depending only on a cost function and an aggregate term have several industrial applications. In this talk, I will briefly formalize a framework for such aggregative minimization problems, as well as develop two methods in order to find approximate solutions. The first one is based on a cutting-plane method on the dual problem. The second is a primal-dual algorithm proposed by A. Chambolle and T. Pock on the saddle-point formulation. I will also link my works with the existing ones found in the paper of C. Wang and the paper of J.-F. Bonnans et al.
Biography. Thibault Moquet is a PhD student in Applied Mathematics at the L2S, CentraleSupélec, under the supervision of Guilherme Mazanti and Laurent Pfeiffer. He received his Bachelor’s Degree in Pure and Applied Mathematics from the Université Paris-Sud (now Université Paris-Saclay) in 2019 and his Master’s Degree in Optimization from the Université Paris-Saclay in 2022. He also passed the Agrégation in Mathematics in 2021. His current main research interests are Convex Optimization and Mean-Field Games.
14h00–15h00 — Salle du conseil (L2S)
New results on asymptotic consensus formation in graphon dynamics
Abstract. The analysis of consensus formation is not a completely fresh topic, as its investigation started around the end of the 1990’s in physics- and engineering-related research communities. In the beginning of the years 2000s, some general and rather sharp conditions ensuring the convergence to consensus for finite-dimensional multiagent systems had been put forth in several independent works.
More recently, a trend of mathematical research at the interface between the analysis of collective dynamics and kinetic theory focused on the generalisation of these stability results to various kinds of macroscopic approximations of multiagent systems, defined e.g. via the meanfield procedure. While being both meaningful and flexible, the latter only accounted for symmetric interaction topologies, and thus excluded a large number of asymmetric models which are relevant in applications. In order to paliate this intrinsic limitation, a couple of recent papers have started studying the question of consensus formation in graphon dynamics, which are inherently better-suited to handling asymmetric interactions.
In this talk, I will discuss two families of sufficient conditions ensuring the exponential convergence towards consensus for macroscopic approximations of first-order multiagent dynamics described by graphons, derived in collaboration with N. Pouradier Duteil and M. Sigalotti. These latter will involve suitable infinite-dimensional generalisations of the so-called scrambling coefficient and algebraic connectivity of the interaction topology, which are known to be intimately connected to the asymptotic behaviour of cooperative systems in the finite-dimensional setting.
Biography. Benoît Bonnet-Weill est chargé de recherche au LAAS-CNRS où il travaille sur les thématiques du transport optimal et du contrôle multi-agent depuis qu’il a rejoint le laboratoire en 2021. Après avoir obtenu un double diplôme de l’ENSTA Paris et de l’Université Paris-Saclay dans les domaines de l’optimisation et de la commande en 2016, il a effectué un doctorat sur le thème du contrôle optimal dans les espaces de Wasserstein sous la supervision de Francesco Rossi et de Maxime Hauray, partageant son temps entre les universités de Marseille et de Padoue. De sa soutenance fin 2019 jusqu’à son recrutement au CNRS en novembre 2021, il a effectué deux postdoctorats à Sorbonne Université, le premier à l’Institut de Mathématiques de Jussieu sous la supervision d’Hélène Frankowska, et le second au Laboratoire Jacques-Louis Lions où il a collaboré avec Mario Sigalotti et Nastassia Pouradier Duteil.
