Source Conditions for Non-Quadratic Tikhonov Regularization. (17th August 2020)

• Record Type: Journal Article
• Authors: Grasmair, Markus
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 11(2020)
• Page Start: 1352
• Page End: 1372
• Publication Date: 2020-08-17
• Subjects: convergence rates -- Linear inverse problems -- source conditions -- Tikhonov regularization; 47A52 -- 49N45 -- 65J20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1772289
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we consider convex Tikhonov regularization for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be employed in order to derive convergence rates in terms of the Bregman distance, assuming some stronger convexity properties of either the regularization term or its convex conjugate. In the special case of quadratic regularization, we are able to reproduce the whole range of Hölder type convergence rates known from classical theory.