On the implementation of a primal-dual algorithm for second order time-dependent Mean Field Games with local couplings

Briceño-Arias, Luis; Kalise, Ddante; Kobeissi, Ziad; Laurière, Mathieu; Mateos González, Álvaro; Silva, Francisco

Abstract

We study a numerical approximation of a time-dependent Mean Field Game (MFG) system with local couplings. The discretization we consider stems from a variational approach described in [14] for the stationary problem and leads to the finite difference scheme introduced by Achdou and Capuzzo-Dolcetta in [3]. In order to solve the finite dimensional variational problems, in [14] the authors implement the primal-dual algorithm introduced by Chambolle and Pock in [20], whose core consists in iteratively solving linear systems and applying a proximity operator. We apply that method to time-dependent MFG and, for large viscosity parameters, we improve the linear system solution by replacing the direct approach used in [14] by suitable preconditioned iterative algorithms.

Citation

Briceño-Arias, L., Kalise, D., Kobeissi, Z., Laurière, M., Mateos González, Á., & Silva, F. (2019). On the implementation of a primal-dual algorithm for second order time-dependent Mean Field Games with local couplings. ESAIM. Proceedings and surveys, 65, 330-348. https://doi.org/10.1051/proc/201965330

• Journal Article Type: Article
• Acceptance Date: Nov 23, 2018
• Online Publication Date: Apr 2, 2019
• Publication Date: Feb 1, 2019
• Deposit Date: Sep 2, 2019
• Publicly Available Date: Sep 3, 2019
• Journal: ESAIM: Proceedings and Surveys
• Print ISSN: 2267-3059
• Peer Reviewed: Peer Reviewed
• Volume: 65
• Pages: 330-348
• DOI: https://doi.org/10.1051/proc/201965330
• Public URL: https://nottingham-repository.worktribe.com/output/2522843
• Publisher URL: https://www.esaim-proc.org/articles/proc/abs/2019/01/proc196514/proc196514.html