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Bilevel Optimal Control: Existence Results and Stationarity Conditions

In: Bilevel Optimization

Author

Listed:
  • Patrick Mehlitz

    (Brandenburgische Technische Universität Cottbus-Senftenberg)

  • Gerd Wachsmuth

    (Brandenburgische Technische Universität Cottbus-Senftenberg)

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.

Suggested Citation

  • Patrick Mehlitz & Gerd Wachsmuth, 2020. "Bilevel Optimal Control: Existence Results and Stationarity Conditions," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 451-484, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-52119-6_16
    DOI: 10.1007/978-3-030-52119-6_16
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    Cited by:

    1. Markus Friedemann & Felix Harder & Gerd Wachsmuth, 2023. "Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods," Journal of Global Optimization, Springer, vol. 86(4), pages 1025-1061, August.

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