Maximal Solutions of Sparse Analysis Regularization

Abdessamad Barbara (), Abderrahim Jourani () and Samuel Vaiter ()
Additional contact information
Abdessamad Barbara: Université de Bourgogne Franche-Comté
Abderrahim Jourani: Université de Bourgogne Franche-Comté
Samuel Vaiter: Université de Bourgogne Franche-Comté

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 2, No 2, 374-396

Abstract: Abstract This paper deals with the non-uniqueness of the solutions of an analysis—Lasso regularization. Most previous works in this area are concerned with the case, where the solution set is a singleton, or to derive guarantees to enforce uniqueness. Our main contribution consists in providing a geometrical interpretation of a solution with a maximal analysis support: such a solution abides in the relative interior of the solution set. Our result allows us to provide a way to exhibit a maximal solution using a primal-dual interior point algorithm.

Keywords: Lasso; Analysis sparsity; Uniqueness; Inverse problem; Support identification; Barrier penalization; 90C25; 49J52 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1385-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1385-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1385-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().