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    Por favor, use este identificador para citar o enlazar este ítem:https://uvadoc.uva.es/handle/10324/63850

    Título
    Optimal Bounds for Numerical Approximations of Infinite Horizon Problems Based on Dynamic Programming Approach
    Autor
    Frutos Baraja, Francisco Javier deAutoridad UVA Orcid
    Novo, Julia
    Año del Documento
    2023-04-30
    Editorial
    SIAM
    Descripción
    Producción Científica
    Documento Fuente
    SIAM Journal on Control and Optimization, 61 (2023), 361-510
    Zusammenfassung
    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 similar assumptions 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 behaviour $1/h$ from the bound $O(k/h)$ have not been observed.
    Materias (normalizadas)
    Matemáticas
    Análisis Numérico
    Materias Unesco
    1206 Análisis Numérico
    1207.05 Programación Dinámica
    Palabras Clave
    Dynamic programming
    Hamilton-Jacobi-Bellman equation
    optimal control
    error analysis
    ISSN
    0363-0129
    Revisión por pares
    SI
    DOI
    10.1137/21M1459290
    Patrocinador
    Spanish MINECO, grant PID2019-104141GB-I00
    Junta de Castilla y León, grant VA169P20 co-finanzed by FEDER (EU) funds
    Version del Editor
    https://epubs.siam.org/doi/epdf/10.1137/21M1459290
    Propietario de los Derechos
    Society for Industrial and Applied Mathematics
    Idioma
    spa
    URI
    https://uvadoc.uva.es/handle/10324/63850
    Tipo de versión
    info:eu-repo/semantics/acceptedVersion
    Derechos
    restrictedAccess
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    • DEP51 - Artículos de revista [147]
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    frutos_novo_revised_5b.pdf
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