A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise

Christian Clason, Bangti Jin

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Original languageEnglish (US)
Pages (from-to)505-536
Number of pages32
JournalSIAM Journal on Imaging Sciences
Volume5
Issue number2
DOIs
StatePublished - Jan 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This author’s work was supported by the Austrian Science Fund (FWF) under grantSFB F32 (SFB “Mathematical Optimization and Applications in Biomedical Sciences”).This author’s work was supported by AwardKUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Fingerprint

Dive into the research topics of 'A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise'. Together they form a unique fingerprint.

Cite this