Optimal control problems with $L^0(\Omega)$ constraints: maximum principle and proximal gradient method
Optimization and Control
2022-08-04 v2
Abstract
We investigate optimal control problems with 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 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.
Cite
@article{arxiv.2201.05360,
title = {Optimal control problems with $L^0(\Omega)$ constraints: maximum principle and proximal gradient method},
author = {Daniel Wachsmuth},
journal= {arXiv preprint arXiv:2201.05360},
year = {2022}
}