---
_id: '7577'
abstract:
- lang: eng
text: Weak convergence of inertial iterative method for solving variational inequalities
is the focus of this paper. The cost function is assumed to be non-Lipschitz and
monotone. We propose a projection-type method with inertial terms and give weak
convergence analysis under appropriate conditions. Some test results are performed
and compared with relevant methods in the literature to show the efficiency and
advantages given by our proposed methods.
acknowledgement: The project of the first 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
arxiv: 1
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
citation:
ama: Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type
method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287
apa: Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities
with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287
chicago: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational
Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor &
Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287.
ieee: Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities
with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor
& Francis, pp. 192–216, 2022.
ista: Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with
inertial-type method. Applicable Analysis. 101(1), 192–216.
mla: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities
with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor
& Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287.
short: Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216.
date_created: 2020-03-09T07:06:52Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2024-03-05T14:01:52Z
day: '01'
ddc:
- '510'
- '515'
- '518'
department:
- _id: VlKo
doi: 10.1080/00036811.2020.1736287
ec_funded: 1
external_id:
arxiv:
- '2101.08057'
isi:
- '000518364100001'
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oa: 1
oa_version: Submitted Version
page: 192-216
project:
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call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Applicable Analysis
publication_identifier:
eissn:
- 1563-504X
issn:
- 0003-6811
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak convergence for variational inequalities with inertial-type method
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 101
year: '2022'
...
---
_id: '7925'
abstract:
- lang: eng
text: In this paper, we introduce a relaxed CQ method with alternated inertial step
for solving split feasibility problems. We give convergence of the sequence generated
by our method under some suitable assumptions. Some numerical implementations
from sparse signal and image deblurring are reported to show the efficiency of
our method.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The authors are grateful to the referees for their insightful comments
which have improved the earlier version of the manuscript greatly. The first 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: 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: Aviv
full_name: Gibali, Aviv
last_name: Gibali
citation:
ama: Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities.
Optimization Letters. 2021;15:2109-2126. doi:10.1007/s11590-020-01603-1
apa: Shehu, Y., & Gibali, A. (2021). New inertial relaxed method for solving
split feasibilities. Optimization Letters. Springer Nature. https://doi.org/10.1007/s11590-020-01603-1
chicago: Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving
Split Feasibilities.” Optimization Letters. Springer Nature, 2021. https://doi.org/10.1007/s11590-020-01603-1.
ieee: Y. Shehu and A. Gibali, “New inertial relaxed method for solving split feasibilities,”
Optimization Letters, vol. 15. Springer Nature, pp. 2109–2126, 2021.
ista: Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities.
Optimization Letters. 15, 2109–2126.
mla: Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split
Feasibilities.” Optimization Letters, vol. 15, Springer Nature, 2021, pp.
2109–26, doi:10.1007/s11590-020-01603-1.
short: Y. Shehu, A. Gibali, Optimization Letters 15 (2021) 2109–2126.
date_created: 2020-06-04T11:28:33Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2024-03-07T15:00:43Z
day: '01'
ddc:
- '510'
department:
- _id: VlKo
doi: 10.1007/s11590-020-01603-1
ec_funded: 1
external_id:
isi:
- '000537342300001'
file:
- access_level: open_access
checksum: 63c5f31cd04626152a19f97a2476281b
content_type: application/pdf
creator: kschuh
date_created: 2024-03-07T14:58:51Z
date_updated: 2024-03-07T14:58:51Z
file_id: '15089'
file_name: 2021_OptimizationLetters_Shehu.pdf
file_size: 2148882
relation: main_file
success: 1
file_date_updated: 2024-03-07T14:58:51Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 2109-2126
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: Optimization Letters
publication_identifier:
eissn:
- 1862-4480
issn:
- 1862-4472
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New inertial relaxed method for solving split feasibilities
tmp:
image: /images/cc_by.png
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type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2021'
...
---
_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. Optimization and Engineering. 2021;22:2627-2653.
doi:10.1007/s11081-020-09544-5
apa: 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.
Springer Nature. https://doi.org/10.1007/s11081-020-09544-5
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.” Optimization and Engineering.
Springer Nature, 2021. https://doi.org/10.1007/s11081-020-09544-5.
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,” Optimization and Engineering,
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.” Optimization and Engineering, vol. 22, Springer Nature,
2021, pp. 2627–53, doi:10.1007/s11081-020-09544-5.
short: Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering
22 (2021) 2627–2653.
date_created: 2020-08-03T14:29:57Z
date_published: 2021-02-25T00:00:00Z
date_updated: 2024-03-07T14:39:29Z
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'
...
---
_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. Mathematical Methods
of Operations Research. 2021;93(2):213-242. doi:10.1007/s00186-020-00730-w
apa: Shehu, Y., Iyiola, O. S., Thong, D. V., & Van, N. T. C. (2021). An inertial
subgradient extragradient algorithm extended to pseudomonotone equilibrium problems.
Mathematical Methods of Operations Research. Springer Nature. https://doi.org/10.1007/s00186-020-00730-w
chicago: Shehu, Yekini, Olaniyi S. Iyiola, Duong Viet Thong, and Nguyen Thi Cam
Van. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone
Equilibrium Problems.” Mathematical Methods of Operations Research. Springer
Nature, 2021. https://doi.org/10.1007/s00186-020-00730-w.
ieee: Y. Shehu, O. S. Iyiola, D. V. Thong, and N. T. C. Van, “An inertial subgradient
extragradient algorithm extended to pseudomonotone equilibrium problems,” Mathematical
Methods of Operations Research, 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.” Mathematical Methods of Operations
Research, vol. 93, no. 2, Springer Nature, 2021, pp. 213–42, doi:10.1007/s00186-020-00730-w.
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'
...
---
_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. Networks and Spatial Economics.
2021;21(2):291-323. doi:10.1007/s11067-021-09517-w
apa: Izuchukwu, C., & Shehu, Y. (2021). New inertial projection methods for
solving multivalued variational inequality problems beyond monotonicity. Networks
and Spatial Economics. Springer Nature. https://doi.org/10.1007/s11067-021-09517-w
chicago: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods
for Solving Multivalued Variational Inequality Problems beyond Monotonicity.”
Networks and Spatial Economics. Springer Nature, 2021. https://doi.org/10.1007/s11067-021-09517-w.
ieee: C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued
variational inequality problems beyond monotonicity,” Networks and Spatial
Economics, 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.” Networks
and Spatial Economics, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323,
doi:10.1007/s11067-021-09517-w.
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'
...
---
_id: '9315'
abstract:
- lang: eng
text: We consider inertial iteration methods for Fermat–Weber location problem and
primal–dual three-operator splitting in real Hilbert spaces. To do these, we first
obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of
the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators
in infinite dimensional real Hilbert spaces under some seemingly easy to implement
conditions on the iterative parameters. One of our contributions is that the convergence
analysis and rate of convergence results are obtained using conditions which appear
not complicated and restrictive as assumed in other previous related results in
the literature. We then show that Fermat–Weber location problem and primal–dual
three-operator splitting are special cases of fixed point problem of nonexpansive
mapping and consequently obtain the convergence analysis of inertial iteration
methods for Fermat–Weber location problem and primal–dual three-operator splitting
in real Hilbert spaces. Some numerical implementations are drawn from primal–dual
three-operator splitting to support the theoretical analysis.
acknowledgement: The research of this author is supported by the Postdoctoral Fellowship
from Institute of Science and Technology (IST), Austria.
article_number: '75'
article_processing_charge: No
article_type: original
author:
- first_name: Olaniyi S.
full_name: Iyiola, Olaniyi S.
last_name: Iyiola
- 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, Shehu Y. New convergence results for inertial Krasnoselskii–Mann
iterations in Hilbert spaces with applications. Results in Mathematics.
2021;76(2). doi:10.1007/s00025-021-01381-x
apa: Iyiola, O. S., & Shehu, Y. (2021). New convergence results for inertial
Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results
in Mathematics. Springer Nature. https://doi.org/10.1007/s00025-021-01381-x
chicago: Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial
Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results
in Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s00025-021-01381-x.
ieee: O. S. Iyiola and Y. Shehu, “New convergence results for inertial Krasnoselskii–Mann
iterations in Hilbert spaces with applications,” Results in Mathematics,
vol. 76, no. 2. Springer Nature, 2021.
ista: Iyiola OS, Shehu Y. 2021. New convergence results for inertial Krasnoselskii–Mann
iterations in Hilbert spaces with applications. Results in Mathematics. 76(2),
75.
mla: Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial
Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results
in Mathematics, vol. 76, no. 2, 75, Springer Nature, 2021, doi:10.1007/s00025-021-01381-x.
short: O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021).
date_created: 2021-04-11T22:01:14Z
date_published: 2021-03-25T00:00:00Z
date_updated: 2023-10-10T09:47:33Z
day: '25'
department:
- _id: VlKo
doi: 10.1007/s00025-021-01381-x
external_id:
isi:
- '000632917700001'
intvolume: ' 76'
isi: 1
issue: '2'
language:
- iso: eng
month: '03'
oa_version: None
publication: Results in Mathematics
publication_identifier:
eissn:
- 1420-9012
issn:
- 1422-6383
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert
spaces with applications
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 76
year: '2021'
...
---
_id: '9365'
abstract:
- lang: eng
text: In this paper, we propose a new iterative method with alternated inertial
step for solving split common null point problem in real Hilbert spaces. We obtain
weak convergence of the proposed iterative algorithm. Furthermore, we introduce
the notion of bounded linear regularity property for the split common null point
problem and obtain the linear convergence property for the new algorithm under
some mild assumptions. Finally, we provide some numerical examples to demonstrate
the performance and efficiency of the proposed method.
acknowledgement: 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).
article_processing_charge: No
article_type: original
author:
- first_name: Ferdinard U.
full_name: Ogbuisi, Ferdinard U.
last_name: Ogbuisi
- first_name: Yekini
full_name: Shehu, Yekini
id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
last_name: Shehu
orcid: 0000-0001-9224-7139
- first_name: Jen Chih
full_name: Yao, Jen Chih
last_name: Yao
citation:
ama: Ogbuisi FU, Shehu Y, Yao JC. Convergence analysis of new inertial method for
the split common null point problem. Optimization. 2021. doi:10.1080/02331934.2021.1914035
apa: Ogbuisi, F. U., Shehu, Y., & Yao, J. C. (2021). Convergence analysis of
new inertial method for the split common null point problem. Optimization.
Taylor and Francis. https://doi.org/10.1080/02331934.2021.1914035
chicago: Ogbuisi, Ferdinard U., Yekini Shehu, and Jen Chih Yao. “Convergence Analysis
of New Inertial Method for the Split Common Null Point Problem.” Optimization.
Taylor and Francis, 2021. https://doi.org/10.1080/02331934.2021.1914035.
ieee: F. U. Ogbuisi, Y. Shehu, and J. C. Yao, “Convergence analysis of new inertial
method for the split common null point problem,” Optimization. Taylor and
Francis, 2021.
ista: Ogbuisi FU, Shehu Y, Yao JC. 2021. Convergence analysis of new inertial method
for the split common null point problem. Optimization.
mla: Ogbuisi, Ferdinard U., et al. “Convergence Analysis of New Inertial Method
for the Split Common Null Point Problem.” Optimization, Taylor and Francis,
2021, doi:10.1080/02331934.2021.1914035.
short: F.U. Ogbuisi, Y. Shehu, J.C. Yao, Optimization (2021).
date_created: 2021-05-02T22:01:29Z
date_published: 2021-04-14T00:00:00Z
date_updated: 2023-10-10T09:48:41Z
day: '14'
department:
- _id: VlKo
doi: 10.1080/02331934.2021.1914035
ec_funded: 1
external_id:
isi:
- '000640109300001'
isi: 1
language:
- iso: eng
month: '04'
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
publication_identifier:
eissn:
- 1029-4945
issn:
- 0233-1934
publication_status: published
publisher: Taylor and Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence analysis of new inertial method for the split common null point
problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_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. Optimization Methods and Software. 2021. doi:10.1080/10556788.2021.1924715
apa: Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2021). Reflected three-operator
splitting method for monotone inclusion problem. Optimization Methods and Software.
Taylor and Francis. https://doi.org/10.1080/10556788.2021.1924715
chicago: Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator
Splitting Method for Monotone Inclusion Problem.” Optimization Methods and
Software. Taylor and Francis, 2021. https://doi.org/10.1080/10556788.2021.1924715.
ieee: O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting
method for monotone inclusion problem,” Optimization Methods and Software.
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.” Optimization Methods and Software, Taylor and Francis,
2021, doi:10.1080/10556788.2021.1924715.
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'
...
---
_id: '8077'
abstract:
- lang: eng
text: The projection methods with vanilla inertial extrapolation step for variational
inequalities have been of interest to many authors recently due to the improved
convergence speed contributed by the presence of inertial extrapolation step.
However, it is discovered that these projection methods with inertial steps lose
the Fejér monotonicity of the iterates with respect to the solution, which is
being enjoyed by their corresponding non-inertial projection methods for variational
inequalities. This lack of Fejér monotonicity makes projection methods with vanilla
inertial extrapolation step for variational inequalities not to converge faster
than their corresponding non-inertial projection methods at times. Also, it has
recently been proved that the projection methods with vanilla inertial extrapolation
step may provide convergence rates that are worse than the classical projected
gradient methods for strongly convex functions. In this paper, we introduce projection
methods with alternated inertial extrapolation step for solving variational inequalities.
We show that the sequence of iterates generated by our methods converges weakly
to a solution of the variational inequality under some appropriate conditions.
The Fejér monotonicity of even subsequence is recovered in these methods and linear
rate of convergence is obtained. The numerical implementations of our methods
compared with some other inertial projection methods show that our method is more
efficient and outperforms some of these inertial projection methods.
acknowledgement: The authors are grateful to the two anonymous referees for their
insightful comments and suggestions which have improved the earlier version of the
manuscript greatly. The first author has received funding from the European Research
Council (ERC) under the European Union Seventh Framework Programme (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
citation:
ama: 'Shehu Y, Iyiola OS. Projection methods with alternating inertial steps for
variational inequalities: Weak and linear convergence. Applied Numerical Mathematics.
2020;157:315-337. doi:10.1016/j.apnum.2020.06.009'
apa: 'Shehu, Y., & Iyiola, O. S. (2020). Projection methods with alternating
inertial steps for variational inequalities: Weak and linear convergence. Applied
Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2020.06.009'
chicago: 'Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating
Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” Applied
Numerical Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.apnum.2020.06.009.'
ieee: 'Y. Shehu and O. S. Iyiola, “Projection methods with alternating inertial
steps for variational inequalities: Weak and linear convergence,” Applied Numerical
Mathematics, vol. 157. Elsevier, pp. 315–337, 2020.'
ista: 'Shehu Y, Iyiola OS. 2020. Projection methods with alternating inertial steps
for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics.
157, 315–337.'
mla: 'Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating
Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” Applied
Numerical Mathematics, vol. 157, Elsevier, 2020, pp. 315–37, doi:10.1016/j.apnum.2020.06.009.'
short: Y. Shehu, O.S. Iyiola, Applied Numerical Mathematics 157 (2020) 315–337.
date_created: 2020-07-02T09:02:33Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2023-08-22T07:50:43Z
day: '01'
ddc:
- '510'
department:
- _id: VlKo
doi: 10.1016/j.apnum.2020.06.009
ec_funded: 1
external_id:
isi:
- '000564648400018'
file:
- access_level: open_access
checksum: 87d81324a62c82baa925c009dfcb0200
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oa_version: Submitted Version
page: 315-337
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Applied Numerical Mathematics
publication_identifier:
issn:
- 0168-9274
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Projection methods with alternating inertial steps for variational inequalities:
Weak and linear convergence'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 157
year: '2020'
...
---
_id: '7161'
abstract:
- lang: eng
text: In this paper, we introduce an inertial projection-type method with different
updating strategies for solving quasi-variational inequalities with strongly monotone
and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions,
we establish different strong convergence results for the proposed algorithm.
Primary numerical experiments demonstrate the potential applicability of our scheme
compared with some related methods in the literature.
acknowledgement: We are grateful to the anonymous referees and editor whose insightful
comments helped to considerably improve an earlier version of this paper. The research
of the first author is supported by an ERC Grant from the Institute of Science and
Technology (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: Aviv
full_name: Gibali, Aviv
last_name: Gibali
- first_name: Simone
full_name: Sagratella, Simone
last_name: Sagratella
citation:
ama: Shehu Y, Gibali A, Sagratella S. Inertial projection-type methods for solving
quasi-variational inequalities in real Hilbert spaces. Journal of Optimization
Theory and Applications. 2020;184:877–894. doi:10.1007/s10957-019-01616-6
apa: Shehu, Y., Gibali, A., & Sagratella, S. (2020). Inertial projection-type
methods for solving quasi-variational inequalities in real Hilbert spaces. Journal
of Optimization Theory and Applications. Springer Nature. https://doi.org/10.1007/s10957-019-01616-6
chicago: Shehu, Yekini, Aviv Gibali, and Simone Sagratella. “Inertial Projection-Type
Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” Journal
of Optimization Theory and Applications. Springer Nature, 2020. https://doi.org/10.1007/s10957-019-01616-6.
ieee: Y. Shehu, A. Gibali, and S. Sagratella, “Inertial projection-type methods
for solving quasi-variational inequalities in real Hilbert spaces,” Journal
of Optimization Theory and Applications, vol. 184. Springer Nature, pp. 877–894,
2020.
ista: Shehu Y, Gibali A, Sagratella S. 2020. Inertial projection-type methods for
solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization
Theory and Applications. 184, 877–894.
mla: Shehu, Yekini, et al. “Inertial Projection-Type Methods for Solving Quasi-Variational
Inequalities in Real Hilbert Spaces.” Journal of Optimization Theory and Applications,
vol. 184, Springer Nature, 2020, pp. 877–894, doi:10.1007/s10957-019-01616-6.
short: Y. Shehu, A. Gibali, S. Sagratella, Journal of Optimization Theory and Applications
184 (2020) 877–894.
date_created: 2019-12-09T21:33:44Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-09-06T11:27:15Z
day: '01'
ddc:
- '518'
- '510'
- '515'
department:
- _id: VlKo
doi: 10.1007/s10957-019-01616-6
ec_funded: 1
external_id:
isi:
- '000511805200009'
file:
- access_level: open_access
checksum: 9f6dc6c6bf2b48cb3a2091a9ed5feaf2
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creator: dernst
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language:
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month: '03'
oa: 1
oa_version: Submitted Version
page: 877–894
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Journal of Optimization Theory and Applications
publication_identifier:
eissn:
- 1573-2878
issn:
- 0022-3239
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inertial projection-type methods for solving quasi-variational inequalities
in real Hilbert spaces
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 184
year: '2020'
...
---
_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. Numerical Algorithms. 2020;84:365-388.
doi:10.1007/s11075-019-00758-y
apa: Shehu, Y., Li, X.-H., & Dong, Q.-L. (2020). An efficient projection-type
method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms.
Springer Nature. https://doi.org/10.1007/s11075-019-00758-y
chicago: Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type
Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical
Algorithms. Springer Nature, 2020. https://doi.org/10.1007/s11075-019-00758-y.
ieee: Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for
monotone variational inequalities in Hilbert spaces,” Numerical Algorithms,
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.” Numerical Algorithms, vol. 84, Springer
Nature, 2020, pp. 365–88, doi:10.1007/s11075-019-00758-y.
short: Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.
date_created: 2019-06-27T20:09:33Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-08-17T13:51:18Z
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
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date_updated: 2020-07-14T12:47:34Z
file_id: '6927'
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language:
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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'
...
---
_id: '7000'
abstract:
- lang: eng
text: The main contributions of this paper are the proposition and the convergence
analysis of a class of inertial projection-type algorithm for solving variational
inequality problems in real Hilbert spaces where the underline operator is monotone
and uniformly continuous. We carry out a unified analysis of the proposed method
under very mild assumptions. In particular, weak convergence of the generated
sequence is established and nonasymptotic O(1 / n) rate of convergence is established,
where n denotes the iteration counter. We also present some experimental results
to illustrate the profits gained by introducing the inertial extrapolation steps.
article_number: '161'
article_processing_charge: No
article_type: original
arxiv: 1
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: 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, Iyiola OS, Li X-H, Dong Q-L. Convergence analysis of projection method
for variational inequalities. Computational and Applied Mathematics. 2019;38(4).
doi:10.1007/s40314-019-0955-9
apa: Shehu, Y., Iyiola, O. S., Li, X.-H., & Dong, Q.-L. (2019). Convergence
analysis of projection method for variational inequalities. Computational and
Applied Mathematics. Springer Nature. https://doi.org/10.1007/s40314-019-0955-9
chicago: Shehu, Yekini, Olaniyi S. Iyiola, Xiao-Huan Li, and Qiao-Li Dong. “Convergence
Analysis of Projection Method for Variational Inequalities.” Computational
and Applied Mathematics. Springer Nature, 2019. https://doi.org/10.1007/s40314-019-0955-9.
ieee: Y. Shehu, O. S. Iyiola, X.-H. Li, and Q.-L. Dong, “Convergence analysis of
projection method for variational inequalities,” Computational and Applied
Mathematics, vol. 38, no. 4. Springer Nature, 2019.
ista: Shehu Y, Iyiola OS, Li X-H, Dong Q-L. 2019. Convergence analysis of projection
method for variational inequalities. Computational and Applied Mathematics. 38(4),
161.
mla: Shehu, Yekini, et al. “Convergence Analysis of Projection Method for Variational
Inequalities.” Computational and Applied Mathematics, vol. 38, no. 4, 161,
Springer Nature, 2019, doi:10.1007/s40314-019-0955-9.
short: Y. Shehu, O.S. Iyiola, X.-H. Li, Q.-L. Dong, Computational and Applied Mathematics
38 (2019).
date_created: 2019-11-12T12:41:44Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2023-08-30T07:20:32Z
day: '01'
ddc:
- '510'
- '515'
- '518'
department:
- _id: VlKo
doi: 10.1007/s40314-019-0955-9
ec_funded: 1
external_id:
arxiv:
- '2101.09081'
isi:
- '000488973100005'
has_accepted_license: '1'
intvolume: ' 38'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s40314-019-0955-9
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Computational and Applied Mathematics
publication_identifier:
eissn:
- 1807-0302
issn:
- 2238-3603
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence analysis of projection method for variational inequalities
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 38
year: '2019'
...
---
_id: '6596'
abstract:
- lang: eng
text: It is well known that many problems in image recovery, signal processing,
and machine learning can be modeled as finding zeros of the sum of maximal monotone
and Lipschitz continuous monotone operators. Many papers have studied forward-backward
splitting methods for finding zeros of the sum of two monotone operators in Hilbert
spaces. Most of the proposed splitting methods in the literature have been proposed
for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert
spaces. In this paper, we consider splitting methods for finding zeros of the
sum of maximal monotone operators and Lipschitz continuous monotone operators
in Banach spaces. We obtain weak and strong convergence results for the zeros
of the sum of maximal monotone and Lipschitz continuous monotone operators in
Banach spaces. Many already studied problems in the literature can be considered
as special cases of this paper.
article_number: '138'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Yekini
full_name: Shehu, Yekini
id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87
last_name: Shehu
orcid: 0000-0001-9224-7139
citation:
ama: Shehu Y. Convergence results of forward-backward algorithms for sum of monotone
operators in Banach spaces. Results in Mathematics. 2019;74(4). doi:10.1007/s00025-019-1061-4
apa: Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum
of monotone operators in Banach spaces. Results in Mathematics. Springer.
https://doi.org/10.1007/s00025-019-1061-4
chicago: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for
Sum of Monotone Operators in Banach Spaces.” Results in Mathematics. Springer,
2019. https://doi.org/10.1007/s00025-019-1061-4.
ieee: Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone
operators in Banach spaces,” Results in Mathematics, vol. 74, no. 4. Springer,
2019.
ista: Shehu Y. 2019. Convergence results of forward-backward algorithms for sum
of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138.
mla: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum
of Monotone Operators in Banach Spaces.” Results in Mathematics, vol. 74,
no. 4, 138, Springer, 2019, doi:10.1007/s00025-019-1061-4.
short: Y. Shehu, Results in Mathematics 74 (2019).
date_created: 2019-06-29T10:11:30Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2023-08-28T12:26:22Z
day: '01'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.1007/s00025-019-1061-4
ec_funded: 1
external_id:
arxiv:
- '2101.09068'
isi:
- '000473237500002'
file:
- access_level: open_access
checksum: c6d18cb1e16fc0c36a0e0f30b4ebbc2d
content_type: application/pdf
creator: kschuh
date_created: 2019-07-03T15:20:40Z
date_updated: 2020-07-14T12:47:34Z
file_id: '6605'
file_name: Springer_2019_Shehu.pdf
file_size: 466942
relation: main_file
file_date_updated: 2020-07-14T12:47:34Z
has_accepted_license: '1'
intvolume: ' 74'
isi: 1
issue: '4'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
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: Results in Mathematics
publication_identifier:
eissn:
- 1420-9012
issn:
- 1422-6383
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence results of forward-backward algorithms for sum of monotone operators
in Banach spaces
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 74
year: '2019'
...