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Bilevel optimal control: existence results and stationarity conditions

  • The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential equations. Such models are referred to as bilevel optimal control problems. Here, we first review some different features of bilevel optimal control including important applications, existence results, solution approaches, and optimality conditions. Afterwards, we focus on a specific problem class where parameters appearing in the objective functional of an optimal control problem of partial differential equations have to be reconstructed. After verifying the existence of solutions, necessary optimality conditions are derived by exploiting the optimal value function of the underlying parametric optimal control problem in the context of a relaxation approach.

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Metadaten
Author: Patrick MehlitzORCiD, Gerd WachsmuthORCiD
DOI:https://doi.org/10.1007/978-3-030-52119-6_16
ISBN:978-3-030-52119-6
ISBN:978-3-030-52118-9
Title of the source (English):Bilevel Optimization
Publisher:Springer Nature
Place of publication:Schweiz
Document Type:Part of a book (chapter)
Language:English
Year of publication:2020
Tag:Bilevel optimal control; Existence results; Inverse optimal control; Stationarity conditions
First Page:451
Last Page:484
Series ; volume number:Springer Optimization and Its Applications ; 161
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung
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