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Bilevel Optimization pp 451–484Cite as

Bilevel Optimal Control: Existence Results and Stationarity Conditions

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 161))

Abstract

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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Authors and Affiliations

  1. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Patrick Mehlitz & Gerd Wachsmuth

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  1. Patrick Mehlitz
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  2. Gerd Wachsmuth
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Correspondence to Patrick Mehlitz .

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Editors and Affiliations

  1. Institute of Numerical Mathematics and Optimization, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

  2. School of Mathematical Sciences, University of Southampton, Southampton, UK

    Alain Zemkoho

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Mehlitz, P., Wachsmuth, G. (2020). Bilevel Optimal Control: Existence Results and Stationarity Conditions. In: Dempe, S., Zemkoho, A. (eds) Bilevel Optimization. Springer Optimization and Its Applications, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-030-52119-6_16

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