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Source Conditions for Non-Quadratic Tikhonov Regularization
Numerical Functional Analysis and Optimization ( IF 1.2 ) Pub Date : 2020-06-12 , DOI: 10.1080/01630563.2020.1772289
Markus Grasmair 1
Affiliation  

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.

中文翻译:

非二次 Tikhonov 正则化的源条件

摘要 在本文中,我们考虑了 Hilbert 空间上线性算子方程解的凸 Tikhonov 正则化。我们表明,假设正则化项或其凸共轭具有更强的凸性,可以采用标准分数源条件来根据 Bregman 距离导出收敛率。在二次正则化的特殊情况下,我们能够重现经典理论中已知的整个 Hölder 型收敛率范围。
更新日期:2020-06-12
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