| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 68 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2022058 | |
| 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: hoppe@ins.uni-bonn.de
Received:
31
January
2022
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
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