Skip to main content

Research Repository

See what's under the surface

Advanced Search

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

Authors

Luis Briceño-Arias

Ziad Kobeissi

Mathieu Laurière

Álvaro Mateos González

Francisco Silva



Contributors

B. Bouchard
Editor

J.-F. Chassagneux
Editor

F. Delarue
Editor

E. Gobet
Editor

J. Lelong
Editor

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.

Journal Article Type Article
Publication Date Feb 1, 2019
Journal ESAIM: Proceedings and Surveys
Print ISSN 2267-3059
Peer Reviewed Peer Reviewed
Volume 65
Pages 330-348
APA6 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. doi:10.1051/proc/201965330
DOI https://doi.org/10.1051/proc/201965330
Publisher URL https://www.esaim-proc.org/articles/proc/abs/2019/01/proc196514/proc196514.html

Files

On the implementation of a primal-dual algorithm for second order (788 Kb)
PDF





You might also like



Downloadable Citations

;