Volume 28, 2022
|Number of page(s)||31|
|Published online||03 November 2022|
Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization*
Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Friedrich-Hirzebruch-Allee 7, 53115 Bonn, Germany
** Corresponding author: firstname.lastname@example.org
Accepted: 12 September 2022
We prove first- and second-order optimality conditions for sparse, purely time-dependent optimal control problems governed by a quasilinear parabolic PDE. In particular, we analyze sparsity patterns of the optimal controls induced by different sparsity enforcing functionals in the purely timedependent control case and illustrate them by numerical examples. Our findings are based on results obtained by abstraction of well known techniques from the literature.
Mathematics Subject Classification: 49K20 / 49J52 / 35K59 / 65K10
Key words: Optimal control / (directional) sparsity / purely time-dependent control / second-order optimality conditions / quasilinear parabolic equations
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.