A topological derivative-based algorithm to solve optimal control problems with $L^0(\Omega)$ control cost
Optimization and Control
2024-08-07 v7
Abstract
In this paper, we consider optimization problems with -cost of the controls. Here, we take the support of the control as independent optimization variable. Topological derivatives of the corresponding value function with respect to variations of the support are derived. These topological derivatives are used in a novel gradient descent algorithm with Armijo line-search. Under suitable assumptions, the algorithm produces a minimizing sequence.
Cite
@article{arxiv.2211.12246,
title = {A topological derivative-based algorithm to solve optimal control problems with $L^0(\Omega)$ control cost},
author = {Daniel Wachsmuth},
journal= {arXiv preprint arXiv:2211.12246},
year = {2024}
}