An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions

Radu Ioan Boţ (), Ernö Robert Csetnek () and Szilárd Csaba László ()
Additional contact information
Radu Ioan Boţ: University of Vienna
Ernö Robert Csetnek: University of Vienna
Szilárd Csaba László: Technical University of Cluj-Napoca

EURO Journal on Computational Optimization, 2016, vol. 4, issue 1, No 2, 3-25

Abstract: Abstract We propose a forward–backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Łojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.

Keywords: Nonsmooth optimization; Limiting subdifferential; Kurdyka-Łojasiewicz inequality; Bregman distance; Inertial proximal algorithm; 90C26; 90C30; 65K10 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://link.springer.com/10.1007/s13675-015-0045-8 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:eurjco:v:4:y:2016:i:1:d:10.1007_s13675-015-0045-8

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/13675

DOI: 10.1007/s13675-015-0045-8

Access Statistics for this article

EURO Journal on Computational Optimization is currently edited by Martine C. Labbé

More articles in EURO Journal on Computational Optimization from Springer, EURO - The Association of European Operational Research Societies
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().