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

DOI10.1515/jiip-2015-0038zbMath1338.65152OpenAlexW2399213862MaRDI QIDQ299030

Stefan Kindermann

Publication date: 22 June 2016

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip-2015-0038

zbMATH Keywords

convergence ratesTikhonov regularizationBregman distancevariational regularization

Mathematics Subject Classification ID

Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (10)

A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations ⋮ On the existence and stability of minimizers for generalized Tikhonov functionals with general similarity data ⋮ A note on the approximate symmetry of Bregman distances ⋮ Penalty-based smoothness conditions in convex variational regularization ⋮ Choice of the parameters in a primal-dual algorithm for Bregman iterated variational regularization ⋮ The Kurdyka–Łojasiewicz Inequality as Regularity Condition ⋮ Existence of variational source conditions for nonlinear inverse problems in Banach spaces ⋮ Convergence analysis of (statistical) inverse problems under conditional stability estimates ⋮ Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints ⋮ Variational regularization theory based on image space approximation rates

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