---
_id: '8196'
abstract:
- lang: eng
  text: This paper aims to obtain a strong convergence result for a Douglas–Rachford
    splitting method with inertial extrapolation step for finding a zero of the sum
    of two set-valued maximal monotone operators without any further assumption of
    uniform monotonicity on any of the involved maximal monotone operators. Furthermore,
    our proposed method is easy to implement and the inertial factor in our proposed
    method is a natural choice. Our method of proof is of independent interest. Finally,
    some numerical implementations are given to confirm the theoretical analysis.
acknowledgement: Open access funding provided by Institute of Science and Technology
  (IST Austria). The project of Yekini Shehu has received funding from the European
  Research Council (ERC) under the European Union’s Seventh Framework Program (FP7—2007–2013)
  (Grant Agreement No. 616160). The authors are grateful to the anonymous referees
  and the handling Editor for their comments and suggestions which have improved the
  earlier version of the manuscript greatly.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Yekini
  full_name: Shehu, Yekini
  id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
  last_name: Shehu
  orcid: 0000-0001-9224-7139
- first_name: Qiao-Li
  full_name: Dong, Qiao-Li
  last_name: Dong
- first_name: Lu-Lu
  full_name: Liu, Lu-Lu
  last_name: Liu
- first_name: Jen-Chih
  full_name: Yao, Jen-Chih
  last_name: Yao
citation:
  ama: Shehu Y, Dong Q-L, Liu L-L, Yao J-C. New strong convergence method for the
    sum of two maximal monotone operators. <i>Optimization and Engineering</i>. 2021;22:2627-2653.
    doi:<a href="https://doi.org/10.1007/s11081-020-09544-5">10.1007/s11081-020-09544-5</a>
  apa: Shehu, Y., Dong, Q.-L., Liu, L.-L., &#38; Yao, J.-C. (2021). New strong convergence
    method for the sum of two maximal monotone operators. <i>Optimization and Engineering</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s11081-020-09544-5">https://doi.org/10.1007/s11081-020-09544-5</a>
  chicago: Shehu, Yekini, Qiao-Li Dong, Lu-Lu Liu, and Jen-Chih Yao. “New Strong Convergence
    Method for the Sum of Two Maximal Monotone Operators.” <i>Optimization and Engineering</i>.
    Springer Nature, 2021. <a href="https://doi.org/10.1007/s11081-020-09544-5">https://doi.org/10.1007/s11081-020-09544-5</a>.
  ieee: Y. Shehu, Q.-L. Dong, L.-L. Liu, and J.-C. Yao, “New strong convergence method
    for the sum of two maximal monotone operators,” <i>Optimization and Engineering</i>,
    vol. 22. Springer Nature, pp. 2627–2653, 2021.
  ista: Shehu Y, Dong Q-L, Liu L-L, Yao J-C. 2021. New strong convergence method for
    the sum of two maximal monotone operators. Optimization and Engineering. 22, 2627–2653.
  mla: Shehu, Yekini, et al. “New Strong Convergence Method for the Sum of Two Maximal
    Monotone Operators.” <i>Optimization and Engineering</i>, vol. 22, Springer Nature,
    2021, pp. 2627–53, doi:<a href="https://doi.org/10.1007/s11081-020-09544-5">10.1007/s11081-020-09544-5</a>.
  short: Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering
    22 (2021) 2627–2653.
corr_author: '1'
date_created: 2020-08-03T14:29:57Z
date_published: 2021-02-25T00:00:00Z
date_updated: 2024-11-04T13:52:38Z
day: '25'
ddc:
- '510'
department:
- _id: VlKo
doi: 10.1007/s11081-020-09544-5
ec_funded: 1
external_id:
  isi:
  - '000559345400001'
file:
- access_level: open_access
  content_type: application/pdf
  creator: dernst
  date_created: 2020-08-03T15:24:39Z
  date_updated: 2020-08-03T15:24:39Z
  file_id: '8197'
  file_name: 2020_OptimizationEngineering_Shehu.pdf
  file_size: 2137860
  relation: main_file
  success: 1
file_date_updated: 2020-08-03T15:24:39Z
has_accepted_license: '1'
intvolume: '        22'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 2627-2653
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '616160'
  name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Optimization and Engineering
publication_identifier:
  eissn:
  - 1573-2924
  issn:
  - 1389-4420
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New strong convergence method for the sum of two maximal monotone operators
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2021'
...