Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR 2018: 0.881
5-year IMPACT FACTOR: 1.170

CiteScore 2018: 0.91

SCImago Journal Rank (SJR) 2018: 0.430
Source Normalized Impact per Paper (SNIP) 2018: 0.969

Mathematical Citation Quotient (MCQ) 2017: 0.49

Online
ISSN
1569-3945
See all formats and pricing
More options …
Volume 21, Issue 5

Issues

Semismooth Newton and quasi-Newton methods in weighted ℓ1-regularization

Pham Quy Muoi / Dinh Nho Hào / Peter Maass / Michael Pidcock
  • Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Wheatley Campus, Wheatley, Oxford OX33 1HX, United Kingdom
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-07-02 | DOI: https://doi.org/10.1515/jip-2013-0031

Abstract.

We investigate semismooth Newton and quasi-Newton methods for minimization problems arising from weighted ℓ1-regularization. We give proofs of the local convergence of these methods and show how their interpretation as active set methods leads to the development of efficient numerical implementations of these algorithms. We also propose and analyze Broyden updates for the semismooth quasi-Newton method. The efficiency of these methods is analyzed and compared with standard implementations. The paper concludes with some numerical examples that include both linear and nonlinear operator equations.

Keywords: Sparsity regularization; nonlinear inverse problems; semismooth Newton method; semismooth quasi-Newton method; Newton derivative

About the article

Received: 2013-04-30

Published Online: 2013-07-02

Published in Print: 2013-10-01


Citation Information: Journal of Inverse and Ill-Posed Problems, Volume 21, Issue 5, Pages 665–693, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0031.

Export Citation

© 2013 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Pham Quy Muoi, Dinh Nho Hào, Sujit Kumar Sahoo, Dongliang Tang, Nguyen Huu Cong, and Cuong Dang
Inverse Problems, 2018, Volume 34, Number 5, Page 055007
[2]
Pham Quy Muoi, Dinh Nho Hào, Peter Maass, and Michael Pidcock
Journal of Computational and Applied Mathematics, 2016, Volume 298, Page 105

Comments (0)

Please log in or register to comment.
Log in