Тип публикации: статья из журнала
Год издания: 2020
Идентификатор DOI: 10.1134/S1995080220120380
Ключевые слова: mean field games, planning task, kolmogorov (fokker–, planck) equation, hamilton–, jacobi–, 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 Hamilton-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.
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)
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