On the Strong Convergence of Halpern Type Proximal Point Algorithm

Hadi Khatibzadeh () and Sajad Ranjbar ()
Additional contact information
Hadi Khatibzadeh: University of Zanjan
Sajad Ranjbar: University of Zanjan

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 2, No 5, 385-396

Abstract: Abstract The main result of this paper is to prove the strong convergence of the sequence generated by the proximal point algorithm of Halpern type to a zero of a maximal monotone operator under the suitable assumptions on the parameters and error. The results extend some of the previous results or give some different conditions for convergence of the sequence. It is also indicated that when the maximal monotone operator is the subdifferential of a convex, proper, and lower semicontinuous function, the results extend all previous results in the literature. We also prove the boundedness of the sequence generated by the algorithm with a weak coercivity condition defined in the paper and without any additional assumptions on the parameters.

Keywords: Proximal-point algorithm; Maximal monotone operator; Strong convergence; Coercive operator; Halpern type algorithm; Subdifferential (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-012-0213-4 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:158:y:2013:i:2:d:10.1007_s10957-012-0213-4

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

DOI: 10.1007/s10957-012-0213-4

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 ().