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Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints

  • In this article we study the regularization of optimization problems by Tikhonov regularization. The optimization problems are subject to pointwise inequality constraints in L²(Ω). We derive a-priori regularization error estimates if the regularization parameter as well as the noise level tend to zero. We rely on an assumption that is a combination of a source condition and of a structural assumption on the active sets. Moreover, we introduce a strategy to choose the regularization parameter in dependence of the noise level. We prove convergence of this parameter choice rule with optimal order.

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Metadaten
Author: Daniel WachsmuthORCiD, Gerd WachsmuthORCiD
ISSN:0324-8569
Title of the source (English):Control and Cybernetics
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2011
Tag:convex constraints; discrepancy principle; non-smooth optimization; regularization error estimates; source condition; sparsity
Volume/Year:40
Issue number:4
First Page:1125
Last Page:1158
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung
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