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Convergence rates for Morozov’s Discrepancy Principle using Variational Inequalities
| Citations: | 7 - 1 self |
BibTeX
@MISC{Anzengruber_convergencerates,
author = {Stephan W Anzengruber and Ronny Ramlau},
title = {Convergence rates for Morozov’s Discrepancy Principle using Variational Inequalities},
year = {}
}
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Abstract
We derive convergence rates for Tikhonov-type regularization with convex penalty terms, where the regularization parameter is chosen according to Morozov’s discrepancy principle and variational inequalities are used to generalize classical source and nonlinearity conditions. Rates are obtained first with respect to the Bregman distance and a Taylor-type distance and those results are combined to derive rates in norm and the penalty term topology. For the special case of the sparsity promoting weighted ℓp-norms as penalty terms and for a searched-for solution, which is known to be sparse, the above results give convergence rates of up to linear order.
Keyphrases
morozov discrepancy principle convergence rate variational inequality penalty term result give convergence rate searched-for solution penalty term topology weighted p-norms nonlinearity condition regularization parameter classical source taylor-type distance linear order bregman distance special case convex penalty term tikhonov-type regularization
