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Local minimization algorithms for dynamic programming equations

Kalise, Dante; Kröner, Axel; Kunisch, Karl

Authors

Axel Kröner

Karl Kunisch



Abstract

© 2016 Society for Industrial and Applied Mathematics. The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible controls. This minimization is often performed by comparison over 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 ℓ1-penalization which lead to sparse controls.

Journal Article Type Article
Publication Date Jun 1, 2016
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7200
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 38
Issue 3
Pages A1587-A1615
APA6 Citation Kalise, D., Kröner, A., & Kunisch, K. (2016). Local minimization algorithms for dynamic programming equations. SIAM Journal on Scientific Computing, 38(3), A1587-A1615. https://doi.org/10.1137/15M1010269
DOI https://doi.org/10.1137/15M1010269
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