On Integer Optimal Control with Total Variation Regularization on Multidimensional Domains
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Publication:6071813
DOI10.1137/22M152116XzbMATH Open1527.49023arXiv2212.12226OpenAlexW4388702193MaRDI QIDQ6071813
Author name not available (Why is that?)
Publication date: 29 November 2023
Published in: (Search for Journal in Brave)
Abstract: We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the weak- and closed in the strict topology in the space of functions of bounded variation. In turn, we derive first-order optimality conditions of the optimal control problem as well as trust-region subproblems with partially linearized model functions using local variations of the level sets of the feasible control functions. We also prove that a recently proposed function space trust-region algorithm -- sequential linear integer programming -- produces sequences of iterates whose limits are first-order optimal points.
Full work available at URL: https://arxiv.org/abs/2212.12226
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