Aggregated occupation measures and linear programming approach to constrained impulse control problems

Alexey Piunovskiy*, Yi Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
17 Downloads (Pure)

Abstract

For a constrained optimal impulse control problem of an abstract dynamical system, we introduce the occupation measures along with the aggregated occupation measures and present two associated linear programs. We prove that the two linear programs are equivalent under appropriate conditions, and each linear program gives rise to an optimal strategy in the original impulse control problem. In particular, we show the absence of the relaxation gap. By means of an example, we also present a detailed comparison of the occupation measures and linear programs introduced here with the related notions in the literature.

Original languageEnglish
Article number125070
Number of pages46
JournalJournal of Mathematical Analysis and Applications
Volume499
Issue number2
Early online date15 Feb 2021
DOIs
Publication statusPublished - 15 Jul 2021

Bibliographical note

Funding Information:
This research was supported by the Royal Society International Exchanges award IE160503 . We would like to thank Prof. A. Plakhov for his initial participation in this work and for his proof of Lemma A.1.

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Constraints
  • Dynamical system
  • Impulse control
  • Linear programming
  • Optimal control
  • Total cost

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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