Optimal control problems with $L^0(\Omega)$ constraints: maximum principle and proximal gradient method

Daniel Wachsmuth

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arXiv · 2201.05360

Optimal control problems with $L^0(\Omega)$ constraints: maximum principle and proximal gradient method

Daniel Wachsmuth

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Abstract

We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation is used that respects the $L^0$ constraint. First, the maximum principle is obtained in integral form, which is then turned into a pointwise form. In addition, an optimization algorithm of proximal gradient type is analyzed. Under some assumptions, the sequence of iterates contains strongly converging subsequences, whose limits are feasible and satisfy a subset of the necessary optimality conditions.

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BibTeX RIS

Daniel Wachsmuth. 2022-01-14. Optimal control problems with $L^0(\Omega)$ constraints: maximum principle and proximal gradient method. https://arxiv.org/abs/2201.05360

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