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Title
Local minimization algorithms for dynamic programming equations
AuthorKalise, Dante ; Kröner, Axel ; Kunisch, Karl In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
SIAM Journal on Scientific Computing, 2016, Vol. 38, Issue 3, page A1587-A1615
PublishedSociety for Industrial and Applied Mathematics, 2016
Edition
Accepted version
LanguageEnglish
Document typeJournal Article
Keywords (EN)dynamic programming / Hamilton-Jacobi-Bellman equations / semi-Lagrangian schemes / first order primal-dual methods / semi-smooth Newton methods
ISSN1064-8275
URNurn:nbn:at:at-ubg:3-3492 Persistent Identifier (URN)
DOI10.1137/15M1010269 
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 The work is publicly available
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Local minimization algorithms for dynamic programming equations [3.57 mb]
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Abstract (English)

The application of the dynamic programming principle in continuous-time optimal control problems leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible controls. In the context of the numerical approximation of such equations, this minimization is often performed by comparison between a finite number of elements of the control set. In this paper we demonstrate the importance of an accurate realization of these minimization problems and propose algorithms by which this can be achieved effectively. The considered class of equations includes nonsmooth control problems with 1penalizations which lead to sparse controls.

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