Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity

Yu Cao (), Yuanheng Wang (), Habib Rehman (), Yekini Shehu () and Jen-Chih Yao ()
Additional contact information
Yu Cao: Zhejiang Normal University
Yuanheng Wang: Zhejiang Normal University
Habib Rehman: Zhejiang Normal University
Yekini Shehu: Zhejiang Normal University
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 11, 256-284

Abstract: Abstract In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the sequence of iterates generated by our proposed splitting algorithm converges weakly to the zero of the considered inclusion problem under mild conditions on the iterative parameters. Several splitting algorithms in the literature are recovered as special cases of our proposed algorithm. Another interesting feature of our algorithm is that one forward evaluation of the Lipschitz continuous monotone operator is utilized at each iteration. Numerical results are given to support the theoretical analysis.

Keywords: Maximal monotone; Lipschitz continuity; Weak convergence; Strong convergence; 90C25; 90C60; 68Q25; 49M25; 90C22 (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02501-7 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:203:y:2024:i:1:d:10.1007_s10957-024-02501-7

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

DOI: 10.1007/s10957-024-02501-7

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 ().