The Euler-Lagrange Approximation of the Mean Field Game for the Planning Problem : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.1134/S1995080220120380

Ключевые слова: mean field games, planning task, kolmogorov (fokker&#8211, planck) equation, hamilton&#8211, jacobi&#8211, bellman equation, numerical solution, hamilton–jacobi–bellman equation, kolmogorov (fokker–planck) equation

Аннотация: The paper presents a finite-difference analogue of the differential problem formulated in terms of the theory of "Mean Field Games" for solving the planning problem of convey to a given state. Here optimization problem is formulated as coupled pair of parabolic partial differential equations of the Kolmogorov (Fokker-Planck) and HaПоказать полностьюmilton-Jacobi-Bellman type. The proposed Euler-Lagrange finite-difference analogue inherits the basic properties of an optimization differential problem at a discrete level. As a result, it can serve as an approximation of the original differential problem when the discretization steps tend to zero, or as a self-contained optimization task with a finite set of participants. For the proposed analogue, the algorithm of monotonous minimization of the value functional is constructed and illustrated on a model economic task.

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Издание

Журнал: LOBACHEVSKII JOURNAL OF MATHEMATICS

Выпуск журнала: Vol. 41, Is. 12

Номера страниц: 2702-2713

ISSN журнала: 19950802

Место издания: NEW YORK

Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER

Персоны

  • Shaydurov V. (Russian Acad Sci, Inst Computat Modeling, Siberian Branch, Krasnoyarsk 660036, Russia; Tianjin Univ Finance & Econ, Tianjin 300222, Peoples R China)
  • Kornienko V. (Russian Acad Sci, Inst Computat Modeling, Siberian Branch, Krasnoyarsk 660036, Russia; Siberian Fed Univ, Krasnoyarsk 660041, Russia)
  • Zhang S. (Tianjin Univ Finance & Econ, Tianjin 300222, Peoples R China)