Journal of Convex Analysis 33 (2026), No. 3&4, 597--614
Copyright Heldermann Verlag 2026
Approximation of Bilevel Optimization Problems Involving an Optimal Control Problem at the Lower Level
Térence Bayen
Avignon Université, Laboratoire de Mathématiques, Avignon, France
terence.bayen@univ-avignon.fr
Francis Mairet
Ifremer, Phytox, Physalg Laboratory, Nantes, France
francis.mairet@ifremer.fr
This work studies a regularization procedure whose goal is the approximation of a solution to a bilevel optimization problem where the lower-level problem is formulated as an optimal control problem. This is done by regularizing the lower-level problem in such a way that an optimal control to the regularized problem can be explicitly computed as a feedback of state and costate functions. Convergence between the regularized problems and the original one is addressed: in particular, it is shown that as the regularization parameter tends to zero, the upper-level objective function computed on the optimal control to the regularized problem converges to the value function associated with the original program. The analysis that is carried out partly relies on the hypothesis that the lower-level problem admits a unique solution.
Keywords: Bilevel optimization, optimal control, Pontryagin maximum principle.
MSC: 34A38, 49A15, 49J53.
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