[2306.14404] Convexification Numerical Method for the Retrospective Problem of Mean Field Games
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Mathematics > Numerical Analysis

arXiv:2306.14404 (math)
[Submitted on 26 Jun 2023 (v1), last revised 29 Jun 2023 (this version, v2)]

Title:Convexification Numerical Method for the Retrospective Problem of Mean Field Games

Authors:Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
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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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2306.14404 [math.NA]
  (or arXiv:2306.14404v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2306.14404

Submission history

From: Michael V. Klibanov [view email]
[v1] Mon, 26 Jun 2023 03:36:20 UTC (1,767 KB)
[v2] Thu, 29 Jun 2023 10:21:02 UTC (3,396 KB)
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