---
_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: '9227'
abstract:
- lang: eng
text: In the multiway cut problem we are given a weighted undirected graph G=(V,E) and
a set T⊆V of k terminals. The goal is to find a minimum weight set of edges E′⊆E with
the property that by removing E′ from G all the terminals become disconnected.
In this paper we present a simple local search approximation algorithm for the
multiway cut problem with approximation ratio 2−2k . We present an experimental
evaluation of the performance of our local search algorithm and show that it greatly
outperforms the isolation heuristic of Dalhaus et al. and it has similar performance
as the much more complex algorithms of Calinescu et al., Sharma and Vondrak, and
Buchbinder et al. which have the currently best known approximation ratios for
this problem.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Andrew
full_name: Bloch-Hansen, Andrew
last_name: Bloch-Hansen
- first_name: Nasim
full_name: Samei, Nasim
id: C1531CAE-36E9-11EA-845F-33AA3DDC885E
last_name: Samei
- first_name: Roberto
full_name: Solis-Oba, Roberto
last_name: Solis-Oba
citation:
ama: 'Bloch-Hansen A, Samei N, Solis-Oba R. Experimental evaluation of a local search
approximation algorithm for the multiway cut problem. In: Conference on Algorithms
and Discrete Applied Mathematics. Vol 12601. Springer Nature; 2021:346-358.
doi:10.1007/978-3-030-67899-9_28'
apa: 'Bloch-Hansen, A., Samei, N., & Solis-Oba, R. (2021). Experimental evaluation
of a local search approximation algorithm for the multiway cut problem. In Conference
on Algorithms and Discrete Applied Mathematics (Vol. 12601, pp. 346–358).
Rupnagar, India: Springer Nature. https://doi.org/10.1007/978-3-030-67899-9_28'
chicago: Bloch-Hansen, Andrew, Nasim Samei, and Roberto Solis-Oba. “Experimental
Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem.”
In Conference on Algorithms and Discrete Applied Mathematics, 12601:346–58.
Springer Nature, 2021. https://doi.org/10.1007/978-3-030-67899-9_28.
ieee: A. Bloch-Hansen, N. Samei, and R. Solis-Oba, “Experimental evaluation of a
local search approximation algorithm for the multiway cut problem,” in Conference
on Algorithms and Discrete Applied Mathematics, Rupnagar, India, 2021, vol.
12601, pp. 346–358.
ista: 'Bloch-Hansen A, Samei N, Solis-Oba R. 2021. Experimental evaluation of a
local search approximation algorithm for the multiway cut problem. Conference
on Algorithms and Discrete Applied Mathematics. CALDAM: Conference on Algorithms
and Discrete Applied Mathematics, LNCS, vol. 12601, 346–358.'
mla: Bloch-Hansen, Andrew, et al. “Experimental Evaluation of a Local Search Approximation
Algorithm for the Multiway Cut Problem.” Conference on Algorithms and Discrete
Applied Mathematics, vol. 12601, Springer Nature, 2021, pp. 346–58, doi:10.1007/978-3-030-67899-9_28.
short: A. Bloch-Hansen, N. Samei, R. Solis-Oba, in:, Conference on Algorithms and
Discrete Applied Mathematics, Springer Nature, 2021, pp. 346–358.
conference:
end_date: 2021-02-13
location: Rupnagar, India
name: 'CALDAM: Conference on Algorithms and Discrete Applied Mathematics'
start_date: 2021-02-11
date_created: 2021-03-07T23:01:25Z
date_published: 2021-01-28T00:00:00Z
date_updated: 2023-10-10T09:29:08Z
day: '28'
department:
- _id: VlKo
doi: 10.1007/978-3-030-67899-9_28
intvolume: ' 12601'
language:
- iso: eng
month: '01'
oa_version: None
page: 346-358
publication: Conference on Algorithms and Discrete Applied Mathematics
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030678982'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Experimental evaluation of a local search approximation algorithm for the multiway
cut problem
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12601
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: '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'
...