---
_id: '9234'
abstract:
- lang: eng
  text: In this paper, we present two new inertial projection-type methods for solving
    multivalued variational inequality problems in finite-dimensional spaces. We establish
    the convergence of the sequence generated by these methods when the multivalued
    mapping associated with the problem is only required to be locally bounded without
    any monotonicity assumption. Furthermore, the inertial techniques that we employ
    in this paper are quite different from the ones used in most papers. Moreover,
    based on the weaker assumptions on the inertial factor in our methods, we derive
    several special cases of our methods. Finally, we present some experimental results
    to illustrate the profits that we gain by introducing the inertial extrapolation
    steps.
acknowledgement: 'The authors sincerely thank the Editor-in-Chief and anonymous referees
  for their careful reading, constructive comments and fruitful suggestions that help
  improve the manuscript. The research of the first author is supported by the National
  Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral
  Fellowship; Grant Number: 120784). The first author also acknowledges the financial
  support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical
  Sciences (CoE-MaSS) Postdoctoral Fellowship. The second 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). Open Access funding provided
  by Institute of Science and Technology (IST Austria).'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Chinedu
  full_name: Izuchukwu, Chinedu
  last_name: Izuchukwu
- first_name: Yekini
  full_name: Shehu, Yekini
  id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
  last_name: Shehu
  orcid: 0000-0001-9224-7139
citation:
  ama: Izuchukwu C, Shehu Y. New inertial projection methods for solving multivalued
    variational inequality problems beyond monotonicity. <i>Networks and Spatial Economics</i>.
    2021;21(2):291-323. doi:<a href="https://doi.org/10.1007/s11067-021-09517-w">10.1007/s11067-021-09517-w</a>
  apa: Izuchukwu, C., &#38; Shehu, Y. (2021). New inertial projection methods for
    solving multivalued variational inequality problems beyond monotonicity. <i>Networks
    and Spatial Economics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11067-021-09517-w">https://doi.org/10.1007/s11067-021-09517-w</a>
  chicago: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods
    for Solving Multivalued Variational Inequality Problems beyond Monotonicity.”
    <i>Networks and Spatial Economics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s11067-021-09517-w">https://doi.org/10.1007/s11067-021-09517-w</a>.
  ieee: C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued
    variational inequality problems beyond monotonicity,” <i>Networks and Spatial
    Economics</i>, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021.
  ista: Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued
    variational inequality problems beyond monotonicity. Networks and Spatial Economics.
    21(2), 291–323.
  mla: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for
    Solving Multivalued Variational Inequality Problems beyond Monotonicity.” <i>Networks
    and Spatial Economics</i>, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323,
    doi:<a href="https://doi.org/10.1007/s11067-021-09517-w">10.1007/s11067-021-09517-w</a>.
  short: C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323.
date_created: 2021-03-10T12:18:47Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2023-09-05T15:32:32Z
day: '01'
ddc:
- '510'
department:
- _id: VlKo
doi: 10.1007/s11067-021-09517-w
ec_funded: 1
external_id:
  isi:
  - '000625002100001'
file:
- access_level: open_access
  checksum: 22b4253a2e5da843622a2df713784b4c
  content_type: application/pdf
  creator: kschuh
  date_created: 2021-08-11T12:44:16Z
  date_updated: 2021-08-11T12:44:16Z
  file_id: '9884'
  file_name: 2021_NetworksSpatialEconomics_Shehu.pdf
  file_size: 834964
  relation: main_file
  success: 1
file_date_updated: 2021-08-11T12:44:16Z
has_accepted_license: '1'
intvolume: '        21'
isi: 1
issue: '2'
keyword:
- Computer Networks and Communications
- Software
- Artificial Intelligence
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 291-323
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '616160'
  name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Networks and Spatial Economics
publication_identifier:
  eissn:
  - 1572-9427
  issn:
  - 1566-113X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New inertial projection methods for solving multivalued variational inequality
  problems beyond monotonicity
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 21
year: '2021'
...