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Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

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Frick, Klaus ; Grasmair, Markus:
Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities.
In: Inverse Problems. Bd. 28 (2012) Heft 19.
ISSN 0266-5611 ; 1361-6420

Volltext

Link zum Volltext (externe URL): http://dx.doi.org/10.1088/0266-5611/28/10/104005

Kurzfassung/Abstract

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of Hölder type.

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Publikationsform:Artikel
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen/Informatik
Peer-Review-Journal:Ja
Titel an der KU entstanden:Nein
Eingestellt am:19. Dez 2012 07:37
Letzte Änderung:24. Mai 2016 11:19
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/12731/