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Rachid El Idrissi, Lahoussine Lafhim, Youssef Ouakrim, Pontryagin optimality conditions for generalized bilevel optimal control problems with pure state inequality constraints

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DOI: 10.23952/jano.6.2024.2.05
Volume 6, Issue 2, 1 August 2024, Pages 229-248

 

Abstract. In this paper, we study a generalized bilevel optimal control problem that has a variational inequality parametrized by the final state on the follower and pure state constraints on the leader. After reducing the problem with a gap function to an analogous single-level optimal control problem, we focus on the development of a necessary optimality condition of the Pontryagin type. We highlight some significant issues originating from the generalized bilevel structure and its pure state constraints on the leader, which give rise to a degenerated maximum principle in the absence of constraint qualifications. To ensure the nondegeneracy of the derived maximum principle, we employ a partial penalization strategy and a well-known regularity criterion for optimal control problems with pure state constraints.

 

How to Cite this Article:
R. El Idrissi, L. Lafhim, Y. Ouakrim, Pontryagin optimality conditions for generalized bilevel optimal control problems with pure state inequality constraints, J. Appl. Numer. Optim. 6 (2024), 229-248.