Part 1: 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 1: I will show how to transform suitable mean-field game (MFG) systems into infinite-dimensional convex optimization problems. Furthermore, I will present Uzawa’s algorithm and augmented Lagrangian approach for solving convex optimization problems. Finally, I will demonstrate how to apply these methods to approximate solutions of corresponding MFG systems.
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 1: I will show how to transform suitable mean-field game (MFG) systems into infinite-dimensional convex optimization problems. Furthermore, I will present Uzawa’s algorithm and augmented Lagrangian approach for solving convex optimization problems. Finally, I will demonstrate how to apply these methods to approximate solutions of corresponding MFG systems.
Brief Biography
Dr. Levon Nurbekyan is 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. He obtained his Ph.D. in the framework of UT Austin -- Portugal CoLab under supervision of Professors Diogo Gomes and Alessio Figalli. Afterwards, he held postdoctoral and junior researcher positions at Instituto Superior Técnico, National Academy of Sciences of Armenia, and King Abdullah University of Science and Technology. His 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.
Refreshments: Lights snacks will be provided.
