Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization
Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization
View/Date of Publication
01.2022Publisher
Institut für Numerische SimulationPublisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11788
Abstract
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 time-dependent control case and illustrate them by numerical examples. Our findings are based on results obtained by abstraction of well known techniques from the literature.
Subjects
Optimal control, (directional) sparsity, purely time-dependent control, second-order optimality conditions, quasilinear parabolic equations
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1051/cocv/2022058Part of Series
INS Preprints ; 2201Hoppe, Fabian; Neitzel, Ira: Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization. In: INS Preprints, 2201.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11788
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11788
@unpublished{handle:20.500.11811/11788,
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization},
publisher = {Institut für Numerische Simulation},
year = 2022,
month = jan,
INS Preprints},
volume = 2201,
note = {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 time-dependent control case and illustrate them by numerical examples. Our findings are based on results obtained by abstraction of well known techniques from the literature.},
url = {https://hdl.handle.net/20.500.11811/11788}
}
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization},
publisher = {Institut für Numerische Simulation},
year = 2022,
month = jan,
INS Preprints},
volume = 2201,
note = {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 time-dependent control case and illustrate them by numerical examples. Our findings are based on results obtained by abstraction of well known techniques from the literature.},
url = {https://hdl.handle.net/20.500.11811/11788}
}
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