二阶势均场博弈的网格无关方法

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

IMA Journal of Numerical Analysis Pub Date : 2024-09-18 DOI:10.1093/imanum/drae061

Kang Liu, Laurent Pfeiffer

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引用次数: 0

摘要

本文研究了广义弗兰克-沃尔夫（GFW）算法在解决势场和凸二阶均值场博弈时的收敛性。更具体地说，文章分析了均值场博弈系统的离散化对 GFW 算法有效性的影响。文章的重点是作者在之前的研究中引入的θ方案。对于两种不同的步长选择，分别获得了亚线性和线性收敛速率。这些收敛率具有与网格无关的特性：基本收敛常数与离散化参数无关。

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

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.

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来源期刊

IMA Journal of Numerical Analysis 数学-应用数学

CiteScore

5.30

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.