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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 21, Issue 5


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
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Published Online: 2013-07-02 | DOI: https://doi.org/10.1515/jip-2013-0031


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.

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