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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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0928-0219
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Volume 24, Issue 3

Issues

Convex Tikhonov regularization in Banach spaces: New results on convergence rates

Stefan Kindermann
Published Online: 2015-08-29 | DOI: https://doi.org/10.1515/jiip-2015-0038

Abstract

Tikhonov regularization in Banach spaces with convex penalty and convex fidelity term for linear ill-posed operator equations is studied. As a main result, convergence rates in terms of the Bregman distance of the regularized solution to the exact solution is proven by imposing a generalization of the established variational inequality conditions on the exact solution. This condition only involves a decay rate of the difference of the penalty functionals in terms of the residual.

Keywords: Tikhonov regularization; convergence rates; Bregman distance; variational regularization

MSC: 65J20; 47A52

About the article

Received: 2015-04-01

Revised: 2015-06-01

Accepted: 2015-07-28

Published Online: 2015-08-29

Published in Print: 2016-06-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 3, Pages 341–350, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0038.

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[1]
Martin Burger, Tapio Helin, and Hanne Kekkonen
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