---
_id: '8817'
abstract:
- lang: eng
  text: The paper introduces an inertial extragradient subgradient method with self-adaptive
    step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence
    of the proposed method is obtained under the condition that the bifunction is
    pseudomonotone and Lipchitz continuous. Linear convergence is also given when
    the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations
    and comparisons with other related inertial methods are given using test problems
    including a real-world application to Nash–Cournot oligopolistic electricity market
    equilibrium model.
acknowledgement: The authors are grateful to the two referees and the Associate Editor
  for their comments and suggestions which have improved the earlier version of the
  paper greatly. 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).
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: Olaniyi S.
  full_name: Iyiola, Olaniyi S.
  last_name: Iyiola
- first_name: Duong Viet
  full_name: Thong, Duong Viet
  last_name: Thong
- first_name: Nguyen Thi Cam
  full_name: Van, Nguyen Thi Cam
  last_name: Van
citation:
  ama: Shehu Y, Iyiola OS, Thong DV, Van NTC. An inertial subgradient extragradient
    algorithm extended to pseudomonotone equilibrium problems. <i>Mathematical Methods
    of Operations Research</i>. 2021;93(2):213-242. doi:<a href="https://doi.org/10.1007/s00186-020-00730-w">10.1007/s00186-020-00730-w</a>
  apa: Shehu, Y., Iyiola, O. S., Thong, D. V., &#38; Van, N. T. C. (2021). An inertial
    subgradient extragradient algorithm extended to pseudomonotone equilibrium problems.
    <i>Mathematical Methods of Operations Research</i>. Springer Nature. <a href="https://doi.org/10.1007/s00186-020-00730-w">https://doi.org/10.1007/s00186-020-00730-w</a>
  chicago: Shehu, Yekini, Olaniyi S. Iyiola, Duong Viet Thong, and Nguyen Thi Cam
    Van. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone
    Equilibrium Problems.” <i>Mathematical Methods of Operations Research</i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1007/s00186-020-00730-w">https://doi.org/10.1007/s00186-020-00730-w</a>.
  ieee: Y. Shehu, O. S. Iyiola, D. V. Thong, and N. T. C. Van, “An inertial subgradient
    extragradient algorithm extended to pseudomonotone equilibrium problems,” <i>Mathematical
    Methods of Operations Research</i>, vol. 93, no. 2. Springer Nature, pp. 213–242,
    2021.
  ista: Shehu Y, Iyiola OS, Thong DV, Van NTC. 2021. An inertial subgradient extragradient
    algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods
    of Operations Research. 93(2), 213–242.
  mla: Shehu, Yekini, et al. “An Inertial Subgradient Extragradient Algorithm Extended
    to Pseudomonotone Equilibrium Problems.” <i>Mathematical Methods of Operations
    Research</i>, vol. 93, no. 2, Springer Nature, 2021, pp. 213–42, doi:<a href="https://doi.org/10.1007/s00186-020-00730-w">10.1007/s00186-020-00730-w</a>.
  short: Y. Shehu, O.S. Iyiola, D.V. Thong, N.T.C. Van, Mathematical Methods of Operations
    Research 93 (2021) 213–242.
date_created: 2020-11-29T23:01:18Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2023-10-10T09:30:23Z
day: '01'
department:
- _id: VlKo
doi: 10.1007/s00186-020-00730-w
ec_funded: 1
external_id:
  isi:
  - '000590497300001'
intvolume: '        93'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa_version: None
page: 213-242
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '616160'
  name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Mathematical Methods of Operations Research
publication_identifier:
  eissn:
  - 1432-5217
  issn:
  - 1432-2994
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: An inertial subgradient extragradient algorithm extended to pseudomonotone
  equilibrium problems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 93
year: '2021'
...