| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 51 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/cocv/2025037 | |
| Published online | 30 June 2025 | |
Vector-valued integer optimal control with TV regularization: Optimality conditions and algorithmic treatment
Brandenburgische Technische Universität Cottbus–Senftenberg, Institute of Mathematics, 03046 Cottbus, Germany
* Corresponding author: jonas.marko@b-tu.de
Received:
12
November
2024
Accepted:
8
August
2025
We investigate a broad class of integer optimal control problems with vector-valued controls and switching regularization using a total variation functional involving the p-norm, which influences the structure of a solution. We derive optimality conditions of first and second order for the integer optimal control problem via a switching-point reformulation. For the numerical solution, we use a trust-region method utilizing Bellman’s optimality principle for the subproblems. We will show convergence properties of the method and highlight the algorithm’s efficacy on some benchmark examples.
Mathematics Subject Classification: 49K30 / 49L20 / 49M37 / 90C10
Key words: Integer optimal control problem / total variation regularization / trust-region method
© The authors. Published by EDP Sciences, SMAI 2025
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