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Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 1, Pages 27–39 (Mi timm1494)  

This article is cited in 2 scientific papers (total in 2 papers)

Discrete approximation of the Hamilton-Jacobi equation for the value function in an optimal control problem with infinite horizon

A. L. Bagnoa, A. M. Tarasyevba

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: An infinite horizon optimal control problem is considered in which the quality functional contains an index with discount factor under the integral sign. The main feature of the problem is the unbounded index, which allows to analyze economic growth models with linear, power, and logarithmic utility functions. A discrete approximation of the Hamilton-Jacobi equation is explored for constructing the value function of the original problem. The Holder condition and the sublinear growth condition are derived for the solution of the discrete approximation equation. Uniform convergence of solutions of approximation equations to the value function of the optimal control problem is shown. The obtained results can be used to construct grid approximation methods for the value function of an optimal control problem on an infinite time interval. The proposed methods are effective tools in the modeling of economic growth processes.

Keywords: discrete approximation, optimal control, Hamilton-Jacobi equation, viscosity solution, infinite horizon, value function.

DOI: https://doi.org/10.21538/0134-4889-2018-24-1-27-39

Full text: PDF file (220 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.977
MSC: 49K15, 49L25
Received: 01.12.2017

Citation: A. L. Bagno, A. M. Tarasyev, “Discrete approximation of the Hamilton-Jacobi equation for the value function in an optimal control problem with infinite horizon”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 1, 2018, 27–39

Citation in format AMSBIB
\Bibitem{BagTar18}
\by A.~L.~Bagno, A.~M.~Tarasyev
\paper Discrete approximation of the Hamilton-Jacobi equation for the value function in an optimal control problem with infinite horizon
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 1
\pages 27--39
\mathnet{http://mi.mathnet.ru/timm1494}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-1-27-39}
\elib{http://elibrary.ru/item.asp?id=32604042}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. L. Bagno, A. M. Tarasyev, “Estimate for the Accuracy of a Backward Procedure for the Hamilton–Jacobi Equation in an Infinite-Horizon Optimal Control Problem”, Proc. Steklov Inst. Math., 304 (2019), 110–123  mathnet  crossref  crossref  isi  elib
    2. A. L. Bagno, A. M. Tarasev, “Chislennye metody postroeniya funktsii tseny v zadachakh optimalnogo upravleniya na beskonechnom gorizonte”, Izv. IMI UdGU, 53 (2019), 15–26  mathnet  crossref  elib
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