| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 66 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2022059 | |
| Published online | 24 October 2022 | |
Sequential linear integer programming for integer optimal control with total variation regularization*
1
Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
2
Faculty of Mathematics, TU Dortmund University, Dortmund 44227, Germany
** Corresponding author: paul.manns@tu-dortmund.de
Received:
11
June
2021
Accepted:
17
September
2022
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.
Mathematics Subject Classification: 49M05 / 90C10
Key words: Mixed-integer optimal control / total variation
The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan http://energy.gov/downloads/doe-public-access-plan.
© The authors. Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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