A remark on Uzawa's algorithm and an application to mean field games systems

TL;DR

This paper extends Uzawa's algorithm for broader use and applies it to approximate solutions of mean field games systems, demonstrating its effectiveness through numerical experiments on various control problems.

Contribution

It generalizes Uzawa's algorithm and applies it to mean field games, providing new iterative methods for complex control systems.

Findings

Uzawa's algorithm can be used in more general settings.

Numerical results show convergence on mean field games with different controls.

The method effectively approximates solutions to complex control problems.

Abstract

In this paper, we present an extension of Uzawa's algorithm and apply it to build approximating sequences of mean field games systems. We prove that Uzawa's iterations can be used in a more general situation than the one in it is usually used. We then present some numerical results of those iterations on discrete mean field games systems of optimal stopping, impulse control and continuous control.