Daniel Wachsmuth - A topological derivative-based algorithm to solve optimal control problems with $L^0(\Omega)$ control cost
jnsao:12366 - Journal of Nonsmooth Analysis and Optimization, June 26, 2024, Volume 5 - https://doi.org/10.46298/jnsao-2024-12366A topological derivative-based algorithm to solve optimal control
problems with $L^0(\Omega)$ control costArticle
Authors: Daniel Wachsmuth 
1
In this paper, we consider optimization problems with $L^0$-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.
Source: arXiv.org:2211.12246
Volume: Volume 5
Section: Original research articles
Published on: June 26, 2024
Accepted on: June 24, 2024
Submitted on: October 5, 2023
Keywords: Mathematics - Optimization and Control
Classifications
Mathematics Subject Classification 20201
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