Convexification Numerical Method for the Retrospective Problem of Mean Field Games

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-06-14 DOI:10.1007/s00245-024-10152-3

Michael V. Klibanov, Jingzhi Li, Zhipeng Yang

引用次数: 0

Abstract

The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game of infinitely many rational players. In addition to traditional initial and terminal conditions, one extra terminal condition is assumed to be known. Carleman estimates and a Carleman Weight Function play the key role. Numerical experiments demonstrate a good performance for complicated functions. Various versions of the convexification have been actively used by this research team for a number of years to numerically solve coefficient inverse problems.

Abstract Image

查看原文本刊更多论文

平均场博弈回溯问题的凸化数值法

针对二阶均值场博弈系统的一个问题，构建了具有严格确立的全局收敛特性的凸化数值方法。这是一个由无限多理性玩家组成的博弈的回顾分析问题。除了传统的初始条件和终点条件外，还假定已知一个额外的终点条件。卡勒曼估计和卡勒曼权重函数发挥了关键作用。数值实验证明，复杂函数的性能良好。多年来，该研究团队一直积极使用各种版本的凸化方法来数值求解系数反演问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.