---
_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
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'
file:
- access_level: open_access
checksum: 869efe8cb09505dfa6012f67d20db63d
content_type: application/pdf
creator: dernst
date_created: 2020-10-12T10:42:54Z
date_updated: 2021-03-16T23:30:06Z
embargo: 2021-03-15
file_id: '8648'
file_name: 2020_ApplicAnalysis_Shehu.pdf
file_size: 4282586
relation: main_file
file_date_updated: 2021-03-16T23:30:06Z
has_accepted_license: '1'
intvolume: ' 101'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 192-216
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
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: '10072'
abstract:
- lang: eng
text: The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combinatorics
which can be used to establish the existence of objects that satisfy certain properties.
The breakthrough paper of Moser and Tardos and follow-up works revealed that the
LLL has intimate connections with a class of stochastic local search algorithms
for finding such desirable objects. In particular, it can be seen as a sufficient
condition for this type of algorithms to converge fast. Besides conditions for
existence of and fast convergence to desirable objects, one may naturally ask
further questions regarding properties of these algorithms. For instance, "are
they parallelizable?", "how many solutions can they output?", "what is the expected
"weight" of a solution?", etc. These questions and more have been answered for
a class of LLL-inspired algorithms called commutative. In this paper we introduce
a new, very natural and more general notion of commutativity (essentially matrix
commutativity) which allows us to show a number of new refined properties of LLL-inspired
local search algorithms with significantly simpler proofs.
acknowledgement: "Fotis Iliopoulos: This material is based upon work directly supported
by the IAS Fund for Math and indirectly supported by the National Science Foundation
Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations
expressed in this material are those of the author(s) and do not necessarily reflect
the views of the National Science Foundation. This work is also supported by the
National Science Foundation Grant No. CCF-1815328.\r\nVladimir Kolmogorov: Supported
by the European Research Council under the European Unions Seventh Framework Programme
(FP7/2007-2013)/ERC grant agreement no 616160."
alternative_title:
- LIPIcs
article_number: '31'
article_processing_charge: Yes
author:
- first_name: David G.
full_name: Harris, David G.
last_name: Harris
- first_name: Fotis
full_name: Iliopoulos, Fotis
last_name: Iliopoulos
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the
algorithmic Lovász Local Lemma. In: Approximation, Randomization, and Combinatorial
Optimization. Algorithms and Techniques. Vol 207. Schloss Dagstuhl - Leibniz
Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31'
apa: 'Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2021). A new notion of
commutativity for the algorithmic Lovász Local Lemma. In Approximation, Randomization,
and Combinatorial Optimization. Algorithms and Techniques (Vol. 207). Virtual:
Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31'
chicago: Harris, David G., Fotis Iliopoulos, and Vladimir Kolmogorov. “A New Notion
of Commutativity for the Algorithmic Lovász Local Lemma.” In Approximation,
Randomization, and Combinatorial Optimization. Algorithms and Techniques,
Vol. 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31.
ieee: D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity
for the algorithmic Lovász Local Lemma,” in Approximation, Randomization, and
Combinatorial Optimization. Algorithms and Techniques, Virtual, 2021, vol.
207.
ista: 'Harris DG, Iliopoulos F, Kolmogorov V. 2021. A new notion of commutativity
for the algorithmic Lovász Local Lemma. Approximation, Randomization, and Combinatorial
Optimization. Algorithms and Techniques. APPROX/RANDOM: Approximation Algorithms
for Combinatorial Optimization Problems/ Randomization and Computation, LIPIcs,
vol. 207, 31.'
mla: Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic
Lovász Local Lemma.” Approximation, Randomization, and Combinatorial Optimization.
Algorithms and Techniques, vol. 207, 31, Schloss Dagstuhl - Leibniz Zentrum
für Informatik, 2021, doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31.
short: D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization,
and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl -
Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-08-18
location: Virtual
name: 'APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/
Randomization and Computation'
start_date: 2021-08-16
date_created: 2021-10-03T22:01:22Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2022-03-18T10:08:25Z
day: '15'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.4230/LIPIcs.APPROX/RANDOM.2021.31
ec_funded: 1
external_id:
arxiv:
- '2008.05569'
file:
- access_level: open_access
checksum: 9d2544d53aa5b01565c6891d97a4d765
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-06T13:51:54Z
date_updated: 2021-10-06T13:51:54Z
file_id: '10098'
file_name: 2021_LIPIcs_Harris.pdf
file_size: 804472
relation: main_file
success: 1
file_date_updated: 2021-10-06T13:51:54Z
has_accepted_license: '1'
intvolume: ' 207'
language:
- iso: eng
month: '09'
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: Approximation, Randomization, and Combinatorial Optimization. Algorithms
and Techniques
publication_identifier:
isbn:
- 978-3-9597-7207-5
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new notion of commutativity for the algorithmic Lovász Local Lemma
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: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 207
year: '2021'
...
---
_id: '10552'
abstract:
- lang: eng
text: We study a class of convex-concave saddle-point problems of the form minxmaxy⟨Kx,y⟩+fP(x)−h∗(y)
where K is a linear operator, fP is the sum of a convex function f with a Lipschitz-continuous
gradient and the indicator function of a bounded convex polytope P, and h∗ is
a convex (possibly nonsmooth) function. Such problem arises, for example, as a
Lagrangian relaxation of various discrete optimization problems. Our main assumptions
are the existence of an efficient linear minimization oracle (lmo) for fP and
an efficient proximal map for h∗ which motivate the solution via a blend of proximal
primal-dual algorithms and Frank-Wolfe algorithms. In case h∗ is the indicator
function of a linear constraint and function f is quadratic, we show a O(1/n2)
convergence rate on the dual objective, requiring O(nlogn) calls of lmo. If the
problem comes from the constrained optimization problem minx∈Rd{fP(x)|Ax−b=0}
then we additionally get bound O(1/n2) both on the primal gap and on the infeasibility
gap. In the most general case, we show a O(1/n) convergence rate of the primal-dual
gap again requiring O(nlogn) calls of lmo. To the best of our knowledge, this
improves on the known convergence rates for the considered class of saddle-point
problems. We show applications to labeling problems frequently appearing in machine
learning and computer vision.
acknowledgement: Vladimir Kolmogorov was supported by the European Research Council
under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant
agreement no 616160. Thomas Pock acknowledges support by an ERC grant HOMOVIS, no
640156.
article_processing_charge: No
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Thomas
full_name: Pock, Thomas
last_name: Pock
citation:
ama: 'Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems.
In: 38th International Conference on Machine Learning. ; 2021.'
apa: Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for
saddle problems. In 38th International Conference on Machine Learning.
Virtual.
chicago: Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms
for Saddle Problems.” In 38th International Conference on Machine Learning,
2021.
ieee: V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,”
in 38th International Conference on Machine Learning, Virtual, 2021.
ista: 'Kolmogorov V, Pock T. 2021. One-sided Frank-Wolfe algorithms for saddle problems.
38th International Conference on Machine Learning. ICML: International Conference
on Machine Learning.'
mla: Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for
Saddle Problems.” 38th International Conference on Machine Learning, 2021.
short: V. Kolmogorov, T. Pock, in:, 38th International Conference on Machine Learning,
2021.
conference:
end_date: 2021-07-24
location: Virtual
name: 'ICML: International Conference on Machine Learning'
start_date: 2021-07-18
date_created: 2021-12-16T12:41:20Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2021-12-17T09:06:46Z
day: '01'
department:
- _id: VlKo
ec_funded: 1
external_id:
arxiv:
- '2101.12617'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2101.12617
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: 38th International Conference on Machine Learning
publication_status: published
quality_controlled: '1'
status: public
title: One-sided Frank-Wolfe algorithms for saddle problems
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...
---
_id: '9592'
abstract:
- lang: eng
text: The convex grabbing game is a game where two players, Alice and Bob, alternate
taking extremal points from the convex hull of a point set on the plane. Rational
weights are given to the points. The goal of each player is to maximize the total
weight over all points that they obtain. We restrict the setting to the case of
binary weights. We show a construction of an arbitrarily large odd-sized point
set that allows Bob to obtain almost 3/4 of the total weight. This construction
answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics,
36/1 (2020)]. We also present an arbitrarily large even-sized point set where
Bob can obtain the entirety of the total weight. Finally, we discuss conjectures
about optimum moves in the convex grabbing game for both players in general.
article_processing_charge: No
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Sara
full_name: Nicholson, Sara
last_name: Nicholson
citation:
ama: 'Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing
game on the plane. In: Proceedings of the 33rd Canadian Conference on Computational
Geometry.'
apa: Dvorak, M., & Nicholson, S. (n.d.). Massively winning configurations in
the convex grabbing game on the plane. In Proceedings of the 33rd Canadian
Conference on Computational Geometry. Halifax, NS, Canada.
chicago: Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in
the Convex Grabbing Game on the Plane.” In Proceedings of the 33rd Canadian
Conference on Computational Geometry, n.d.
ieee: M. Dvorak and S. Nicholson, “Massively winning configurations in the convex
grabbing game on the plane,” in Proceedings of the 33rd Canadian Conference
on Computational Geometry, Halifax, NS, Canada.
ista: 'Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing
game on the plane. Proceedings of the 33rd Canadian Conference on Computational
Geometry. CCCG: Canadian Conference on Computational Geometry.'
mla: Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the
Convex Grabbing Game on the Plane.” Proceedings of the 33rd Canadian Conference
on Computational Geometry.
short: M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference
on Computational Geometry, n.d.
conference:
end_date: 2021-08-12
location: Halifax, NS, Canada
name: 'CCCG: Canadian Conference on Computational Geometry'
start_date: 2021-08-10
date_created: 2021-06-22T15:57:11Z
date_published: 2021-06-29T00:00:00Z
date_updated: 2021-08-12T10:57:39Z
day: '29'
ddc:
- '516'
department:
- _id: GradSch
- _id: VlKo
external_id:
arxiv:
- '2106.11247'
file:
- access_level: open_access
checksum: 45accb1de9b7e0e4bb2fbfe5fd3e6239
content_type: application/pdf
creator: mdvorak
date_created: 2021-06-28T20:23:13Z
date_updated: 2021-06-28T20:23:13Z
file_id: '9616'
file_name: Convex-Grabbing-Game_CCCG_proc_version.pdf
file_size: 381306
relation: main_file
success: 1
- access_level: open_access
checksum: 9199cf18c65658553487458cc24d0ab2
content_type: application/pdf
creator: kschuh
date_created: 2021-08-12T10:57:21Z
date_updated: 2021-08-12T10:57:21Z
file_id: '9902'
file_name: Convex-Grabbing-Game_FULL-VERSION.pdf
file_size: 403645
relation: main_file
success: 1
file_date_updated: 2021-08-12T10:57:21Z
has_accepted_license: '1'
keyword:
- convex grabbing game
- graph grabbing game
- combinatorial game
- convex geometry
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '06'
oa: 1
oa_version: Submitted Version
publication: Proceedings of the 33rd Canadian Conference on Computational Geometry
publication_status: accepted
quality_controlled: '1'
status: public
title: Massively winning configurations in the convex grabbing game on the plane
tmp:
image: /image/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
short: CC BY-ND (4.0)
type: conference
user_id: 3E5EF7F0-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'
...