---
_id: '6593'
abstract:
- lang: eng
  text: 'We consider the monotone variational inequality problem in a Hilbert space
    and describe a projection-type method with inertial terms under the following
    properties: (a) The method generates a strongly convergent iteration sequence;
    (b) The method requires, at each iteration, only one projection onto the feasible
    set and two evaluations of the operator; (c) The method is designed for variational
    inequality for which the underline operator is monotone and uniformly continuous;
    (d) The method includes an inertial term. The latter is also shown to speed up
    the convergence in our numerical results. A comparison with some related methods
    is given and indicates that the new method is promising.'
acknowledgement: The research of this author is supported by the ERC grant at the
  IST.
article_processing_charge: No
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: Xiao-Huan
  full_name: Li, Xiao-Huan
  last_name: Li
- first_name: Qiao-Li
  full_name: Dong, Qiao-Li
  last_name: Dong
citation:
  ama: Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone
    variational inequalities in Hilbert spaces. <i>Numerical Algorithms</i>. 2020;84:365-388.
    doi:<a href="https://doi.org/10.1007/s11075-019-00758-y">10.1007/s11075-019-00758-y</a>
  apa: Shehu, Y., Li, X.-H., &#38; Dong, Q.-L. (2020). An efficient projection-type
    method for monotone variational inequalities in Hilbert spaces. <i>Numerical Algorithms</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s11075-019-00758-y">https://doi.org/10.1007/s11075-019-00758-y</a>
  chicago: Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type
    Method for Monotone Variational Inequalities in Hilbert Spaces.” <i>Numerical
    Algorithms</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s11075-019-00758-y">https://doi.org/10.1007/s11075-019-00758-y</a>.
  ieee: Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for
    monotone variational inequalities in Hilbert spaces,” <i>Numerical Algorithms</i>,
    vol. 84. Springer Nature, pp. 365–388, 2020.
  ista: Shehu Y, Li X-H, Dong Q-L. 2020. An efficient projection-type method for monotone
    variational inequalities in Hilbert spaces. Numerical Algorithms. 84, 365–388.
  mla: Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational
    Inequalities in Hilbert Spaces.” <i>Numerical Algorithms</i>, vol. 84, Springer
    Nature, 2020, pp. 365–88, doi:<a href="https://doi.org/10.1007/s11075-019-00758-y">10.1007/s11075-019-00758-y</a>.
  short: Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.
corr_author: '1'
date_created: 2019-06-27T20:09:33Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2024-11-04T13:52:40Z
day: '01'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.1007/s11075-019-00758-y
ec_funded: 1
external_id:
  isi:
  - '000528979000015'
file:
- access_level: open_access
  checksum: bb1a1eb3ebb2df380863d0db594673ba
  content_type: application/pdf
  creator: kschuh
  date_created: 2019-10-01T13:14:10Z
  date_updated: 2020-07-14T12:47:34Z
  file_id: '6927'
  file_name: ExtragradientMethodPaper.pdf
  file_size: 359654
  relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: '        84'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Submitted Version
page: 365-388
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '616160'
  name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Numerical Algorithms
publication_identifier:
  eissn:
  - 1572-9265
  issn:
  - 1017-1398
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: An efficient projection-type method for monotone variational inequalities in
  Hilbert spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 84
year: '2020'
...