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Inexact Newton regularizations with uniformly convex stability terms: a unified convergence analysis

Margotti, Fábio; Pauleti, Marco; Rieder, Andreas 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

We present a unified convergence analysis of inexact Newton regularizations for nonlinear ill-posed problems in Banach spaces. These schemes consist of an outer (Newton) iteration and an inner iteration which provides the update of the current outer iterate. To this end the nonlinear problem is linearized about the current iterate and
the resulting linear system is approximately (inexactly) solved by an inner regularization method. In our analysis we only rely on generic assumptions of the inner methods and we show that a variety of regularization techniques satisfies these assumptions. For instance, gradient-type and iterated-Tikhonov methods are covered. Not only the technique of proof is novel, but also the results obtained, because for the first time uniformly convex
penalty terms stabilize the inner scheme.


Volltext §
DOI: 10.5445/IR/1000157900
Veröffentlicht am 17.04.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 04.2023
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000157900
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 28 S.
Serie CRC 1173 Preprint ; 2023/12
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter nonlinear inverse problems, inexact Newton regularization, convex optimization, Bregman distances, Banach spaces
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