Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach

In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that, considering a time discretization with a positive step size h, an error bound of size h can be proved for the difference between the value fun...

Descripción completa

Detalles Bibliográficos
Autores: De Frutos, Javier, Novo Martín, Julia
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/708440
Acceso en línea:http://hdl.handle.net/10486/708440
https://dx.doi.org/10.1137/21M1459290
Access Level:acceso abierto
Palabra clave:Dynamic Programming
Hamilton-Jacobi-Bellman Equation
Optimal Control
Error Analysis
Matemáticas
id ES_55c04465dbf1a8309fa982680ffbc9f7
oai_identifier_str oai:repositorio.uam.es:10486/708440
network_acronym_str ES
network_name_str España
repository_id_str
spelling Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approachDe Frutos, JavierNovo Martín, JuliaDynamic ProgrammingHamilton-Jacobi-Bellman EquationOptimal ControlError AnalysisMatemáticasIn this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that, considering a time discretization with a positive step size h, an error bound of size h can be proved for the difference between the value function (viscosity solution of the Hamilton-Jacobi-Bellman equation corresponding to the infinite horizon) and the value function of the discrete time problem. However, including also a spatial discretization based on elements of size k, an error bound of size O(k/h) can be found in the literature for the error between the value functions of the continuous problem and the fully discrete problem. In this paper we revise the error bound of the fully discrete method and prove, under assumptions similar to those of the time discrete case, that the error of the fully discrete case is in fact O(h + k), which gives first order in time and space for the method. This error bound matches the numerical experiments of many papers in the literature in which the behavior 1/h from the bound O(k/h) has not been observedResearch supported by Spanish MINECO under grant PID2019-104141GB-I00 and by Junta de Castilla y León under grant VA169P20 co-finanzed by FEDER (EU) funds. Research supported by Spanish MINECO under grant PID2019-104141GB-I00 and by Junta de Castilla y León under grant VA169P20 co-finanzed by FEDER (EU) fundsSociety for Industrial and Applied MathematicsDepartamento de MatemáticasFacultad de Ciencias20222022-10-18research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/708440https://dx.doi.org/10.1137/21M1459290reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7084402026-06-23T12:46:27Z
dc.title.none.fl_str_mv Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
title Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
spellingShingle Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
De Frutos, Javier
Dynamic Programming
Hamilton-Jacobi-Bellman Equation
Optimal Control
Error Analysis
Matemáticas
title_short Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
title_full Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
title_fullStr Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
title_full_unstemmed Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
title_sort Optimal bounds for numerical approximations of infinite horizon problems based on dynamic programming approach
dc.creator.none.fl_str_mv De Frutos, Javier
Novo Martín, Julia
author De Frutos, Javier
author_facet De Frutos, Javier
Novo Martín, Julia
author_role author
author2 Novo Martín, Julia
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Dynamic Programming
Hamilton-Jacobi-Bellman Equation
Optimal Control
Error Analysis
Matemáticas
topic Dynamic Programming
Hamilton-Jacobi-Bellman Equation
Optimal Control
Error Analysis
Matemáticas
description In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that, considering a time discretization with a positive step size h, an error bound of size h can be proved for the difference between the value function (viscosity solution of the Hamilton-Jacobi-Bellman equation corresponding to the infinite horizon) and the value function of the discrete time problem. However, including also a spatial discretization based on elements of size k, an error bound of size O(k/h) can be found in the literature for the error between the value functions of the continuous problem and the fully discrete problem. In this paper we revise the error bound of the fully discrete method and prove, under assumptions similar to those of the time discrete case, that the error of the fully discrete case is in fact O(h + k), which gives first order in time and space for the method. This error bound matches the numerical experiments of many papers in the literature in which the behavior 1/h from the bound O(k/h) has not been observed
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-10-18
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/708440
https://dx.doi.org/10.1137/21M1459290
url http://hdl.handle.net/10486/708440
https://dx.doi.org/10.1137/21M1459290
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408329511469056
score 15,301603

Similares en LA Referencia