Optimal control of quasilinear parabolic PDEs with state-constraints
Optimal control of quasilinear parabolic PDEs with state-constraints
View/Date of Publication
12.2020Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11796
Abstract
We discuss state-constrained optimal control of a quasilinear parabolic PDE. Existence of optimal controls and first-order necessary optimality conditions are derived for a rather general setting including pointwise in time and space constraints on the state. Second-order sufficient optimality conditions are obtained for averaged-in-time and pointwise in space state-constraints under general regularity assumptions for the equation, and for pointwise in time and space state-constraints when restricting in return to a more regular setting for the state equation.
Subjects
second-order sufficient optimality conditions, two-norm discrepancy, optimal control, quasilinear parabolic partial differential equation, pointwise state-constraints
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1137/20M1383951Part of Series
INS Preprints ; 2004Hoppe, Fabian; Neitzel, Ira: Optimal control of quasilinear parabolic PDEs with state-constraints. In: INS Preprints, 2004.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11796
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11796
@unpublished{handle:20.500.11811/11796,
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {Optimal control of quasilinear parabolic PDEs with state-constraints},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = dec,
INS Preprints},
volume = 2004,
note = {We discuss state-constrained optimal control of a quasilinear parabolic PDE. Existence of optimal controls and first-order necessary optimality conditions are derived for a rather general setting including pointwise in time and space constraints on the state. Second-order sufficient optimality conditions are obtained for averaged-in-time and pointwise in space state-constraints under general regularity assumptions for the equation, and for pointwise in time and space state-constraints when restricting in return to a more regular setting for the state equation.},
url = {https://hdl.handle.net/20.500.11811/11796}
}
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {Optimal control of quasilinear parabolic PDEs with state-constraints},
publisher = {Institut für Numerische Simulation (INS)},
year = 2020,
month = dec,
INS Preprints},
volume = 2004,
note = {We discuss state-constrained optimal control of a quasilinear parabolic PDE. Existence of optimal controls and first-order necessary optimality conditions are derived for a rather general setting including pointwise in time and space constraints on the state. Second-order sufficient optimality conditions are obtained for averaged-in-time and pointwise in space state-constraints under general regularity assumptions for the equation, and for pointwise in time and space state-constraints when restricting in return to a more regular setting for the state equation.},
url = {https://hdl.handle.net/20.500.11811/11796}
}
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