A block coordinate variable metric linesearch based proximal gradient method

S. Bonettini (), M. Prato () and S. Rebegoldi ()
Additional contact information
S. Bonettini: Università di Modena e Reggio Emilia
M. Prato: Università di Modena e Reggio Emilia
S. Rebegoldi: Università di Ferrara

Computational Optimization and Applications, 2018, vol. 71, issue 1, No 2, 5-52

Abstract: Abstract In this paper we propose an alternating block version of a variable metric linesearch proximal gradient method. This algorithm addresses problems where the objective function is the sum of a smooth term, whose variables may be coupled, plus a separable part given by the sum of two or more convex, possibly nonsmooth functions, each depending on a single block of variables. Our approach is characterized by the possibility of performing several proximal gradient steps for updating every block of variables and by the Armijo backtracking linesearch for adaptively computing the steplength parameter. Under the assumption that the objective function satisfies the Kurdyka-Łojasiewicz property at each point of its domain and the gradient of the smooth part is locally Lipschitz continuous, we prove the convergence of the iterates sequence generated by the method. Numerical experience on an image blind deconvolution problem show the improvements obtained by adopting a variable number of inner block iterations combined with a variable metric in the computation of the proximal operator.

Keywords: Alternating optimization; Proximal gradient methods; Kurdyka-Łojasiewicz inequality (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-018-0011-5 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:coopap:v:71:y:2018:i:1:d:10.1007_s10589-018-0011-5

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-018-0011-5

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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