Bilevel Optimal Control: Existence Results and Stationarity Conditions

Patrick Mehlitz () and Gerd Wachsmuth ()
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Patrick Mehlitz: Brandenburgische Technische Universität Cottbus-Senftenberg
Gerd Wachsmuth: Brandenburgische Technische Universität Cottbus-Senftenberg

Chapter Chapter 16 in Bilevel Optimization, 2020, pp 451-484 from Springer

Abstract: 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.

Keywords: Bilevel optimal control; Existence results; Inverse optimal control; Stationarity conditions (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-52119-6_16

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DOI: 10.1007/978-3-030-52119-6_16

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