Convexification Numerical Method for the Retrospective Problem of Mean Field Games

06/26/2023

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by   Michael V. Klibanov, et al.

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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.