Abstract
The dynamic programming approach is applied to impulse control problems. The existence of optimal impulse strategy is deduced from general results on fixed points for monotonic and concave transformations.
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There is a vast literature devoted to impulse control problems. We refer the reader to the monograph by A. Bensoussan and J.-L. Lions [8] and to the author survey [113] for more information and references. Theorem 11.1 is a special case of a result due to M. Robin and Lemma 11.2 to B. Hanouzet and J.L. Joly, see, e.g. J. Zabczyk [113]. The abstract approach to dynamic programming equations based on monotonicity and concavity is due to the author, see J. Zabczyk [103], [104], [108] and references there.
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Zabczyk, J. (2020). Dynamic programming for impulse control. In: Mathematical Control Theory. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44778-6_11
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DOI: https://doi.org/10.1007/978-3-030-44778-6_11
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-44776-2
Online ISBN: 978-3-030-44778-6
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