A mesh-independent method for second-order potential mean field games

Liu K, Pfeiffer L (2025)

Publication Type: Journal article

Publication year: 2025

Journal

IMA Journal of Numerical Analysis Oxford University Press (OUP): Policy A - Oxford Open Option A

Book Volume: 45

Pages Range: 1226-1266

Journal Issue: 2

DOI: 10.1093/imanum/drae061

Abstract

This article investigates the convergence of the Generalized Frank–Wolfe (GFW) algorithm for the resolution of potential and convex second-order mean field games. More specifically, the impact of the discretization of the mean-field-game system on the effectiveness of the GFW algorithm is analyzed. The article focuses on the theta-scheme introduced by the authors in a previous study. A sublinear and a linear rate of convergence are obtained, for two different choices of stepsizes. These rates have the mesh-independence property: the underlying convergence constants are independent of the discretization parameters.

Authors with CRIS profile

Kang Liu Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Université Paris-Saclay FR France (FR)

How to cite

APA:

Liu, K., & Pfeiffer, L. (2025). A mesh-independent method for second-order potential mean field games. IMA Journal of Numerical Analysis, 45(2), 1226-1266. https://doi.org/10.1093/imanum/drae061

MLA:

Liu, Kang, and Laurent Pfeiffer. "A mesh-independent method for second-order potential mean field games." IMA Journal of Numerical Analysis 45.2 (2025): 1226-1266.

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