A new approach to nonlinear constrained Tikhonov regularization

Kazufumi Ito, Bangti Jin

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)105005
JournalInverse Problems
Volume27
Issue number10
DOIs
StatePublished - Sep 16 2011
Externally publishedYes

Fingerprint

Dive into the research topics of 'A new approach to nonlinear constrained Tikhonov regularization'. Together they form a unique fingerprint.

Cite this