Demiclosedness Principles for Generalized Nonexpansive Mappings

Sedi Bartz (), Rubén Campoy () and Hung M. Phan ()
Additional contact information
Sedi Bartz: University of Massachusetts Lowell
Rubén Campoy: University of Massachusetts Lowell
Hung M. Phan: University of Massachusetts Lowell

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 2, 759-778

Abstract: Abstract Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas–Rachford algorithm. We provide extensions of this principle, which are compatible with the framework of more general families of mappings such as cocoercive and conically averaged mappings. As an application, we derive the weak convergence of the shadow sequence generated by the adaptive Douglas–Rachford algorithm.

Keywords: Demiclosedness principle; Cocoercive mapping; Conically averaged mapping; Weak convergence; Douglas–Rachford algorithm; Adaptive Douglas–Rachford algorithm; 47H05; 47J25; 49M27 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-020-01734-6 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:186:y:2020:i:3:d:10.1007_s10957-020-01734-6

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

DOI: 10.1007/s10957-020-01734-6

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 ().