Convergence of the SQP method for quasilinear parabolic optimal control problems
Convergence of the SQP method for quasilinear parabolic optimal control problems
View/Date of Publication
11.2019Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11800
Abstract
Based on the theoretical framework recently proposed by Bonifacius and Neitzel (2018) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method in appropriate function spaces is proven under some common technical restrictions.
Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting L2-local quadratic growth condition influence the notion of “locality” in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.
Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting L2-local quadratic growth condition influence the notion of “locality” in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.
Subjects
optimal control, quasilinear parabolic partial differential equation, sequential quadratic programming, convergence analysis
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/s11081-020-09547-2Part of Series
INS Preprints ; 1907Hoppe, Fabian; Neitzel, Ira: Convergence of the SQP method for quasilinear parabolic optimal control problems. In: INS Preprints, 1907.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11800
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11800
@unpublished{handle:20.500.11811/11800,
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {Convergence of the SQP method for quasilinear parabolic optimal control problems},
publisher = {Institut für Numerische Simulation (INS)},
year = 2019,
month = nov,
INS Preprints},
volume = 1907,
note = {Based on the theoretical framework recently proposed by Bonifacius and Neitzel (2018) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method in appropriate function spaces is proven under some common technical restrictions.
Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting L2-local quadratic growth condition influence the notion of “locality” in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.},
url = {https://hdl.handle.net/20.500.11811/11800}
}
author = {{Fabian Hoppe} and {Ira Neitzel}},
title = {Convergence of the SQP method for quasilinear parabolic optimal control problems},
publisher = {Institut für Numerische Simulation (INS)},
year = 2019,
month = nov,
INS Preprints},
volume = 1907,
note = {Based on the theoretical framework recently proposed by Bonifacius and Neitzel (2018) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method in appropriate function spaces is proven under some common technical restrictions.
Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting L2-local quadratic growth condition influence the notion of “locality” in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.},
url = {https://hdl.handle.net/20.500.11811/11800}
}
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