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 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.
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