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

Alexey Piunovskiy; Yi Zhang

doi:10.1016/j.jmaa.2021.125070

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

Alexey Piunovskiy^*, Yi Zhang

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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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 language	English
Article number	125070
Number of pages	46
Journal	Journal of Mathematical Analysis and Applications
Volume	499
Issue number	2
Early online date	15 Feb 2021
DOIs	https://doi.org/10.1016/j.jmaa.2021.125070
Publication status	Published - 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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PiunovskiyA2021AggregatedAccepted author manuscript, 783 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

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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.",

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AU - Zhang, Yi

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N2 - 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.

AB - 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.

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KW - Dynamical system

KW - Impulse control

KW - Linear programming

KW - Optimal control

KW - Total cost

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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