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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 27, Issue 4


The Ivanov regularized Gauss–Newton method in Banach space with an a posteriori choice of the regularization radius

Barbara KaltenbacherORCID iD: https://orcid.org/0000-0002-3295-6977 / Andrej Klassen / Mario Luiz Previatti de Souza
Published Online: 2019-04-06 | DOI: https://doi.org/10.1515/jiip-2018-0093


In this paper, we consider the iteratively regularized Gauss–Newton method, where regularization is achieved by Ivanov regularization, i.e., by imposing a priori constraints on the solution. We propose an a posteriori choice of the regularization radius, based on an inexact Newton/discrepancy principle approach, prove convergence and convergence rates under a variational source condition as the noise level tends to zero and provide an analysis of the discretization error. Our results are valid in general, possibly nonreflexive Banach spaces, including, e.g., L as a preimage space. The theoretical findings are illustrated by numerical experiments.

Keywords: Nonlinear ill-posed problem; regularization; Newton’s method; Ivanov regularization; method of quasi solutions

MSC 2010: 65F22; 65N20


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About the article

Received: 2018-10-02

Revised: 2019-01-01

Accepted: 2019-02-18

Published Online: 2019-04-06

Published in Print: 2019-08-01

Funding Source: Austrian Science Fund

Award identifier / Grant number: I2271

Award identifier / Grant number: P30054

Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: Cl 487/1-1

Supported by the FWF under grants I2271 and P30054 and by the DFG under grant Cl 487/1-1, as well as partially by the Karl Popper Kolleg “Modeling-Simulation-Optimization”, funded by the Alpen-Adria-Universität Klagenfurt and by the Carinthian Economic Promotion Fund (KWF).

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 539–557, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2018-0093.

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