A distributed Bregman forward-backward algorithm for a class of Nash equilibrium problems

Journal article (2022)

Authors

W. Ananduta Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
S. Grammatico , Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
Research Group
Team Sergio Grammatico (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2022 W. Ananduta, S. Grammatico
DOI: https://doi.org/10.1016/j.ejcon.2022.100686
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Published Date

2022

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sergio Grammatico

Abstract

We present a distributed Nash equilibrium seeking method based on the Bregman forward-backward splitting, which allows us to have a mirror mapping instead of the standard projection as the backward operator. Our main technical contribution is to show convergence to a Nash equilibrium when the game has cocoercive pseudogradient mapping. Furthermore, when the feasible sets of the agents are simplices, a suitable choice of a Legendre function results in an exponentiated pseudogradient method, which, in our numerical experience, performs out the standard projected pseudogradient and dual averaging methods.