Sequential linear integer programming for integer optimal control with total variation regularization
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DOI10.1051/COCV/2022059zbMATH Open1500.49016arXiv2106.13453OpenAlexW3174287382MaRDI QIDQ5043062
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Publication date: 27 October 2022
Published in: (Search for Journal in Brave)
Abstract: 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 allows us to prove the existence of minimizers of the integer optimal control problem. 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.
Full work available at URL: https://arxiv.org/abs/2106.13453
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