Part 2: Variational structures and Fourier approximation techniques for mean-field game systems
Mean-field game (MFG) systems of partial differential equations (PDE) arise in modeling huge populations of indistinguishable rational agents that play non-cooperative differential games. Mathematically, an MFG system comprises of a Hamilton-Jacobi-Bellman PDE coupled with a Kolmogorov-Fokker-Planck PDE in a highly nonlinear fashion. Hence, theoretical and numerical treatments of MFG systems are highly challenging problems. Day 2: I will present new Fourier approximation techniques for nonlocal MFG systems and discuss how these techniques fit the variational framework presented on Day 1. Then I will introduce the Chambolle-Pock primal-dual hybrid gradient optimization method and apply a variant of this method to approximate nonlocal MFG models via Fourier approximation techniques above.
Overview
Abstract
Mean-field game (MFG) systems of partial differential equations (PDE) arise in modeling huge populations of indistinguishable rational agents that play non-cooperative differential games. Mathematically, an MFG system comprises of a Hamilton-Jacobi-Bellman PDE coupled with a Kolmogorov-Fokker-Planck PDE in a highly nonlinear fashion. Hence, theoretical and numerical treatments of MFG systems are highly challenging problems.
Day 2: I will present new Fourier approximation techniques for nonlocal MFG systems and discuss how these techniques fit the variational framework presented on Day 1. Then I will introduce the Chambolle-Pock primal-dual hybrid gradient optimization method and apply a variant of this method to approximate nonlocal MFG models via Fourier approximation techniques above.
Brief Biography
Currently, I am a Visiting Scholar at the Department of Mathematics and Statistics at McGill University and a Simons CRM Scholar at the Centre de Recherches Mathématiques (CRM) at Université de Montréal. I obtained my Ph.D. in the framework of UT Austin -- Portugal CoLab under supervision of Professors Diogo Gomes and Alessio Figalli. Afterwards, I held postdoctoral and junior researcher positions at Instituto Superior Técnico, National Academy of Sciences of Armenia, and King Abdullah University of Science and Technology. My research interests include calculus of variations, optimal control theory, mean-field games, partial differential equations, mathematics applied to machine learning, dynamical systems, and shape optimization problems.
