Monotone inclusion methods for a class of second-order non-potential mean-field games
Optimization and Control
2024-04-01 v1 Numerical Analysis
Numerical Analysis
Abstract
We propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games. Following [Achdou, Capuzzo-Dolcetta, "Mean Field Games: Numerical Methods," SINUM (2010)], we introduce a finite-difference scheme and observe that the scheme represents first-order optimality conditions for a primal-dual pair of monotone inclusions. Based on this observation, we prove that the finite-difference system obtains a solution that can be provably recovered by an extension of the celebrated primal-dual hybrid gradient (PDHG) algorithm.
Keywords
Cite
@article{arxiv.2403.20290,
title = {Monotone inclusion methods for a class of second-order non-potential mean-field games},
author = {Levon Nurbekyan and Siting Liu and Yat Tin Chow},
journal= {arXiv preprint arXiv:2403.20290},
year = {2024}
}