Splitting methods for a class of non-potential mean field games

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-06-30 DOI:10.3934/JDG.2021014

Siting Liu, L. Nurbekyan

引用次数: 10

Abstract

We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field games with applications" [arXiv:2004.12210] to a class of non-potential mean-field game (MFG) systems with mixed couplings. Up to now, splitting methods have been applied to potential MFG systems that can be cast as convex-concave saddle-point problems. Here, we show that a class of non-potential MFG can be cast as primal-dual pairs of monotone inclusions and solved via extensions of convex optimization algorithms such as the primal-dual hybrid gradient (PDHG) algorithm. A critical feature of our approach is in considering dual variables of nonlocal couplings in Fourier or feature spaces.

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一类非势平均场对策的分裂方法

我们将Nurbekyan，Saude“一阶非局部平均场对策的傅立叶近似方法”[Port.Math.75（2018），no.3-4]和Liu，Jacobs，Li，Nurbekyan，Osher“非局部平均域对策的计算方法及其应用”[arXiv:2004-121210]的方法推广到一类具有混合耦合的非势平均场对策（MFG）系统。到目前为止，分裂方法已经被应用于潜在的MFG系统，这些系统可以被铸造为凸凹鞍点问题。在这里，我们证明了一类非势MFG可以被铸造为单调包含的原对偶对，并通过凸优化算法（如原对偶混合梯度（PDHG）算法）的扩展来求解。我们方法的一个关键特征是考虑傅立叶或特征空间中非局部耦合的对偶变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.