---
_id: '9469'
abstract:
- lang: eng
  text: In this paper, we consider reflected three-operator splitting methods for
    monotone inclusion problems in real Hilbert spaces. To do this, we first obtain
    weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected
    Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping
    in real Hilbert spaces under some seemingly easy to implement conditions on the
    iterative parameters. We then apply our results to three-operator splitting for
    the monotone inclusion problem and consequently obtain the corresponding convergence
    analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured
    monotone inclusion problems. Some numerical implementations are drawn from splitting
    methods to support the theoretical analysis.
acknowledgement: The authors are grateful to the anonymous referees and the handling
  Editor for their insightful comments which have improved the earlier version of
  the manuscript greatly. The second author is grateful to the University of Hafr
  Al Batin. The last author has received funding from the European Research Council
  (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant
  agreement No. 616160).
article_processing_charge: No
article_type: original
author:
- first_name: Olaniyi S.
  full_name: Iyiola, Olaniyi S.
  last_name: Iyiola
- first_name: Cyril D.
  full_name: Enyi, Cyril D.
  last_name: Enyi
- first_name: Yekini
  full_name: Shehu, Yekini
  id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
  last_name: Shehu
  orcid: 0000-0001-9224-7139
citation:
  ama: Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for
    monotone inclusion problem. <i>Optimization Methods and Software</i>. 2021. doi:<a
    href="https://doi.org/10.1080/10556788.2021.1924715">10.1080/10556788.2021.1924715</a>
  apa: Iyiola, O. S., Enyi, C. D., &#38; Shehu, Y. (2021). Reflected three-operator
    splitting method for monotone inclusion problem. <i>Optimization Methods and Software</i>.
    Taylor and Francis. <a href="https://doi.org/10.1080/10556788.2021.1924715">https://doi.org/10.1080/10556788.2021.1924715</a>
  chicago: Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator
    Splitting Method for Monotone Inclusion Problem.” <i>Optimization Methods and
    Software</i>. Taylor and Francis, 2021. <a href="https://doi.org/10.1080/10556788.2021.1924715">https://doi.org/10.1080/10556788.2021.1924715</a>.
  ieee: O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting
    method for monotone inclusion problem,” <i>Optimization Methods and Software</i>.
    Taylor and Francis, 2021.
  ista: Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method
    for monotone inclusion problem. Optimization Methods and Software.
  mla: Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone
    Inclusion Problem.” <i>Optimization Methods and Software</i>, Taylor and Francis,
    2021, doi:<a href="https://doi.org/10.1080/10556788.2021.1924715">10.1080/10556788.2021.1924715</a>.
  short: O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software (2021).
date_created: 2021-06-06T22:01:30Z
date_published: 2021-05-12T00:00:00Z
date_updated: 2023-08-08T13:57:43Z
day: '12'
department:
- _id: VlKo
doi: 10.1080/10556788.2021.1924715
ec_funded: 1
external_id:
  isi:
  - '000650507600001'
isi: 1
language:
- iso: eng
month: '05'
oa_version: None
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '616160'
  name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Optimization Methods and Software
publication_identifier:
  eissn:
  - 1029-4937
  issn:
  - 1055-6788
publication_status: published
publisher: Taylor and Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Reflected three-operator splitting method for monotone inclusion problem
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...