Quasi-solution of linear inverse problems in non-reflexive Banach spaces

DOI10.1515/jiip-2018-0026zbMath1490.65109arXiv1803.10168OpenAlexW3103339820WikidataQ129423381 ScholiaQ129423381MaRDI QIDQ1615432

Andrej Klassen, Christian Clason

Publication date: 31 October 2018

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

Full work available at URL: https://arxiv.org/abs/1803.10168

zbMATH Keywords

discrepancy principleinverse source problemparameter choiceIvanov regularization

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items

On the iterative regularization of non-linear illposed problems in \(L^{\infty}\) ⋮ On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements ⋮ The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius ⋮ Generalized Modes in Bayesian Inverse Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the approximation of elliptic control problems with bang-bang controls
• Regularization methods in Banach spaces.
• Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Ill-posed problems with a priori information
• On convergence rates for quasi-solutions of ill-posed problems
• A minimum effort optimal control problem for elliptic PDEs
• Necessary conditions for variational regularization schemes
• Theory and examples of variational regularization with non-metric fitting functionals
• Generalized Bregman distances and convergence rates for non-convex regularization methods
• Lagrange Multiplier Approach to Variational Problems and Applications
• The method of quasi-solutions by Ivanov is the effective method of solving ill-posed problems
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs
• Convergence rates of convex variational regularization
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• PROJECTIVE STRUCTURES, FLAT BUNDLES, AND KÄHLER METRICS ON MODULI SPACES
• Regularization of ill-posed problems in Banach spaces: convergence rates