---
_id: '14448'
abstract:
- lang: eng
text: We consider the problem of solving LP relaxations of MAP-MRF inference problems,
and in particular the method proposed recently in [16], [35]. As a key computational
subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth
convex function over a combinatorial polytope. We propose an efficient implementation
of this subroutine based on in-face Frank-Wolfe directions, introduced in [4]
in a different context. More generally, we define an abstract data structure for
a combinatorial subproblem that enables in-face FW directions, and describe its
specialization for tree-structured MAP-MRF inference subproblems. Experimental
results indicate that the resulting method is the current state-of-art LP solver
for some classes of problems. Our code is available at pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html.
article_processing_charge: No
arxiv: 1
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Kolmogorov V. Solving relaxations of MAP-MRF problems: Combinatorial in-face
Frank-Wolfe directions. In: Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition. Vol 2023. IEEE; 2023:11980-11989.
doi:10.1109/CVPR52729.2023.01153'
apa: 'Kolmogorov, V. (2023). Solving relaxations of MAP-MRF problems: Combinatorial
in-face Frank-Wolfe directions. In Proceedings of the IEEE Computer Society
Conference on Computer Vision and Pattern Recognition (Vol. 2023, pp. 11980–11989).
Vancouver, Canada: IEEE. https://doi.org/10.1109/CVPR52729.2023.01153'
chicago: 'Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial
in-Face Frank-Wolfe Directions.” In Proceedings of the IEEE Computer Society
Conference on Computer Vision and Pattern Recognition, 2023:11980–89. IEEE,
2023. https://doi.org/10.1109/CVPR52729.2023.01153.'
ieee: 'V. Kolmogorov, “Solving relaxations of MAP-MRF problems: Combinatorial in-face
Frank-Wolfe directions,” in Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition, Vancouver, Canada, 2023, vol.
2023, pp. 11980–11989.'
ista: 'Kolmogorov V. 2023. Solving relaxations of MAP-MRF problems: Combinatorial
in-face Frank-Wolfe directions. Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision
and Pattern Recognition vol. 2023, 11980–11989.'
mla: 'Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial
in-Face Frank-Wolfe Directions.” Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition, vol. 2023, IEEE, 2023, pp. 11980–89,
doi:10.1109/CVPR52729.2023.01153.'
short: V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on
Computer Vision and Pattern Recognition, IEEE, 2023, pp. 11980–11989.
conference:
end_date: 2023-06-24
location: Vancouver, Canada
name: 'CVPR: Conference on Computer Vision and Pattern Recognition'
start_date: 2023-06-17
date_created: 2023-10-22T22:01:16Z
date_published: 2023-08-22T00:00:00Z
date_updated: 2023-10-31T12:01:24Z
day: '22'
department:
- _id: VlKo
doi: 10.1109/CVPR52729.2023.01153
external_id:
arxiv:
- '2010.09567'
intvolume: ' 2023'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2010.09567'
month: '08'
oa: 1
oa_version: Preprint
page: 11980-11989
publication: Proceedings of the IEEE Computer Society Conference on Computer Vision
and Pattern Recognition
publication_identifier:
isbn:
- '9798350301298'
issn:
- 1063-6919
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe
directions'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2023
year: '2023'
...
---
_id: '13120'
abstract:
- lang: eng
text: 'We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant.
We defined basic notions of rewrite rules and of words derived by a grammar, and
used grammars to show closure of the class of type-0 languages under four operations:
union, reversal, concatenation, and the Kleene star. The literature mostly focuses
on Turing machine arguments, which are possibly more difficult to formalize. For
the Kleene star, we could not follow the literature and came up with our own grammar-based
construction.'
acknowledgement: "Jasmin Blanchette: This research has received funding from the Netherlands
Organization\r\nfor Scientific Research (NWO) under the Vidi program (project No.
016.Vidi.189.037, Lean Forward).\r\n__\r\nWe thank Vladimir Kolmogorov for making
this collaboration possible. We\r\nthank Václav Končický for discussing ideas about
the Kleene star construction. We thank Patrick Johnson, Floris van Doorn, and Damiano
Testa for their small yet very valuable contributions to our code. We thank Eric
Wieser for simplifying one of our proofs. We thank Mark Summerfield for suggesting
textual improvements. We thank the anonymous reviewers for very helpful comments.
Finally, we thank the Lean community for helping us with various technical issues
and answering many questions. "
alternative_title:
- LIPIcs
article_number: '15'
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Jasmin
full_name: Blanchette, Jasmin
last_name: Blanchette
citation:
ama: 'Dvorak M, Blanchette J. Closure properties of general grammars - formally
verified. In: 14th International Conference on Interactive Theorem Proving.
Vol 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ITP.2023.15'
apa: 'Dvorak, M., & Blanchette, J. (2023). Closure properties of general grammars
- formally verified. In 14th International Conference on Interactive Theorem
Proving (Vol. 268). Bialystok, Poland: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.ITP.2023.15'
chicago: Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars
- Formally Verified.” In 14th International Conference on Interactive Theorem
Proving, Vol. 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.
https://doi.org/10.4230/LIPIcs.ITP.2023.15.
ieee: M. Dvorak and J. Blanchette, “Closure properties of general grammars - formally
verified,” in 14th International Conference on Interactive Theorem Proving,
Bialystok, Poland, 2023, vol. 268.
ista: 'Dvorak M, Blanchette J. 2023. Closure properties of general grammars - formally
verified. 14th International Conference on Interactive Theorem Proving. ITP: International
Conference on Interactive Theorem Proving, LIPIcs, vol. 268, 15.'
mla: Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars
- Formally Verified.” 14th International Conference on Interactive Theorem
Proving, vol. 268, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023, doi:10.4230/LIPIcs.ITP.2023.15.
short: M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive
Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.
conference:
end_date: 2023-08-04
location: Bialystok, Poland
name: 'ITP: International Conference on Interactive Theorem Proving'
start_date: 2023-07-31
date_created: 2023-06-05T07:29:05Z
date_published: 2023-07-27T00:00:00Z
date_updated: 2023-09-25T11:04:29Z
day: '27'
ddc:
- '000'
department:
- _id: GradSch
- _id: VlKo
doi: 10.4230/LIPIcs.ITP.2023.15
external_id:
arxiv:
- '2302.06420'
file:
- access_level: open_access
checksum: 773a0197f05b67feaa6cb1e17ec3642d
content_type: application/pdf
creator: dernst
date_created: 2023-08-07T11:55:43Z
date_updated: 2023-08-07T11:55:43Z
file_id: '13982'
file_name: 2023_LIPIcS_Dvorak.pdf
file_size: 715976
relation: main_file
success: 1
file_date_updated: 2023-08-07T11:55:43Z
has_accepted_license: '1'
intvolume: ' 268'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: 14th International Conference on Interactive Theorem Proving
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959772846'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/madvorak/grammars/tree/publish
scopus_import: '1'
status: public
title: Closure properties of general grammars - formally verified
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: 268
year: '2023'
...
---
_id: '14084'
abstract:
- lang: eng
text: "A central problem in computational statistics is to convert a procedure for
sampling combinatorial objects into a procedure for counting those objects, and
vice versa. We will consider sampling problems which come from Gibbs distributions,
which are families of probability distributions over a discrete space Ω with probability
mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max]
and H(ω) ∈ {0} ∪ [1, n].\r\nThe partition function is the normalization factor
Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log
Z(β_max))/Z(β_min)\r\nWe develop a number of algorithms to estimate the counts
c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²)
samples for integer-valued distributions (ignoring some second-order terms and
parameters), We show this is optimal up to logarithmic factors. We illustrate
with improved algorithms for counting connected subgraphs and perfect matchings
in a graph."
acknowledgement: We thank Heng Guo for helpful explanations of algorithms for sampling
connected subgraphs and matchings, Maksym Serbyn for bringing to our attention the
Wang-Landau algorithm and its use in physics.
alternative_title:
- LIPIcs
article_number: '72'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: David G.
full_name: Harris, David G.
last_name: Harris
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. In:
50th International Colloquium on Automata, Languages, and Programming.
Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.72'
apa: 'Harris, D. G., & Kolmogorov, V. (2023). Parameter estimation for Gibbs
distributions. In 50th International Colloquium on Automata, Languages, and
Programming (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.72'
chicago: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs
Distributions.” In 50th International Colloquium on Automata, Languages, and
Programming, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.72.
ieee: D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,”
in 50th International Colloquium on Automata, Languages, and Programming,
Paderborn, Germany, 2023, vol. 261.
ista: 'Harris DG, Kolmogorov V. 2023. Parameter estimation for Gibbs distributions.
50th International Colloquium on Automata, Languages, and Programming. ICALP:
International Colloquium on Automata, Languages, and Programming, LIPIcs, vol.
261, 72.'
mla: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs
Distributions.” 50th International Colloquium on Automata, Languages, and Programming,
vol. 261, 72, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ICALP.2023.72.
short: D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata,
Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023.
conference:
end_date: 2023-07-14
location: Paderborn, Germany
name: 'ICALP: International Colloquium on Automata, Languages, and Programming'
start_date: 2023-07-10
date_created: 2023-08-20T22:01:14Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-08-21T06:49:11Z
day: '01'
ddc:
- '000'
- '510'
department:
- _id: VlKo
doi: 10.4230/LIPIcs.ICALP.2023.72
external_id:
arxiv:
- '2007.10824'
file:
- access_level: open_access
checksum: 6dee0684245bb1c524b9c955db1e933d
content_type: application/pdf
creator: dernst
date_created: 2023-08-21T06:45:16Z
date_updated: 2023-08-21T06:45:16Z
file_id: '14088'
file_name: 2023_LIPIcsICALP_Harris.pdf
file_size: 917791
relation: main_file
success: 1
file_date_updated: 2023-08-21T06:45:16Z
has_accepted_license: '1'
intvolume: ' 261'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: 50th International Colloquium on Automata, Languages, and Programming
publication_identifier:
isbn:
- '9783959772785'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Parameter estimation for Gibbs distributions
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: 261
year: '2023'
...
---
_id: '10737'
abstract:
- lang: eng
text: We consider two models for the sequence labeling (tagging) problem. The first
one is a Pattern-Based Conditional Random Field (PB), in which the energy of a
string (chain labeling) x=x1…xn∈Dn is a sum of terms over intervals [i,j] where
each term is non-zero only if the substring xi…xj equals a prespecified word
w∈Λ. The second model is a Weighted Context-Free Grammar (WCFG) frequently used
for natural language processing. PB and WCFG encode local and non-local interactions
respectively, and thus can be viewed as complementary. We propose a Grammatical
Pattern-Based CRF model (GPB) that combines the two in a natural way. We argue
that it has certain advantages over existing approaches such as the Hybrid model
of Benedí and Sanchez that combines N-grams and WCFGs. The focus of this paper
is to analyze the complexity of inference tasks in a GPB such as computing MAP.
We present a polynomial-time algorithm for general GPBs and a faster version for
a special case that we call Interaction Grammars.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rustem
full_name: Takhanov, Rustem
id: 2CCAC26C-F248-11E8-B48F-1D18A9856A87
last_name: Takhanov
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: Takhanov R, Kolmogorov V. Combining pattern-based CRFs and weighted context-free
grammars. Intelligent Data Analysis. 2022;26(1):257-272. doi:10.3233/IDA-205623
apa: Takhanov, R., & Kolmogorov, V. (2022). Combining pattern-based CRFs and
weighted context-free grammars. Intelligent Data Analysis. IOS Press. https://doi.org/10.3233/IDA-205623
chicago: Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs
and Weighted Context-Free Grammars.” Intelligent Data Analysis. IOS Press,
2022. https://doi.org/10.3233/IDA-205623.
ieee: R. Takhanov and V. Kolmogorov, “Combining pattern-based CRFs and weighted
context-free grammars,” Intelligent Data Analysis, vol. 26, no. 1. IOS
Press, pp. 257–272, 2022.
ista: Takhanov R, Kolmogorov V. 2022. Combining pattern-based CRFs and weighted
context-free grammars. Intelligent Data Analysis. 26(1), 257–272.
mla: Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and
Weighted Context-Free Grammars.” Intelligent Data Analysis, vol. 26, no.
1, IOS Press, 2022, pp. 257–72, doi:10.3233/IDA-205623.
short: R. Takhanov, V. Kolmogorov, Intelligent Data Analysis 26 (2022) 257–272.
date_created: 2022-02-06T23:01:32Z
date_published: 2022-01-14T00:00:00Z
date_updated: 2023-08-02T14:09:41Z
day: '14'
department:
- _id: VlKo
doi: 10.3233/IDA-205623
external_id:
arxiv:
- '1404.5475'
isi:
- '000749997700015'
intvolume: ' 26'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1404.5475
month: '01'
oa: 1
oa_version: Preprint
page: 257-272
publication: Intelligent Data Analysis
publication_identifier:
eissn:
- 1571-4128
issn:
- 1088-467X
publication_status: published
publisher: IOS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Combining pattern-based CRFs and weighted context-free grammars
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2022'
...
---
_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'
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: '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:
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date_updated: 2024-03-07T14:58:51Z
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intvolume: ' 15'
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language:
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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
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: 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: '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: '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: '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
arxiv: 1
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: '10045'
abstract:
- lang: eng
text: "Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem},
denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize
function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative
costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational
complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai:
if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial
time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed
a theory of discrete convex functions on orientable modular graphs generalizing
several known classes of functions in discrete convex analysis, such as L♮-convex
functions. We consider a more general version of the problem in which unary functions
fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where
set F⊆(V2) is fixed. We extend the complexity classification above by providing
an explicit condition on (μ,F) for the problem to be tractable. In order to prove
the tractability part, we generalize Hirai's theory and define a larger class
of discrete convex functions. It covers, in particular, another well-known class
of functions, namely submodular functions on an integer lattice. Finally, we improve
the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n"
article_number: '2109.10203'
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete
convexity. arXiv. doi:10.48550/arXiv.2109.10203
apa: Dvorak, M., & Kolmogorov, V. (n.d.). Generalized minimum 0-extension problem
and discrete convexity. arXiv. https://doi.org/10.48550/arXiv.2109.10203
chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension
Problem and Discrete Convexity.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2109.10203.
ieee: M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and
discrete convexity,” arXiv. .
ista: Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete
convexity. arXiv, 2109.10203.
mla: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem
and Discrete Convexity.” ArXiv, 2109.10203, doi:10.48550/arXiv.2109.10203.
short: M. Dvorak, V. Kolmogorov, ArXiv (n.d.).
date_created: 2021-09-27T10:48:23Z
date_published: 2021-09-21T00:00:00Z
date_updated: 2023-05-03T10:40:16Z
day: '21'
ddc:
- '004'
department:
- _id: GradSch
- _id: VlKo
doi: 10.48550/arXiv.2109.10203
external_id:
arxiv:
- '2109.10203'
file:
- access_level: open_access
checksum: e7e83065f7bc18b9c188bf93b5ca5db6
content_type: application/pdf
creator: mdvorak
date_created: 2021-09-27T10:54:51Z
date_updated: 2021-09-27T10:54:51Z
file_id: '10046'
file_name: Generalized-0-Ext.pdf
file_size: 603672
relation: main_file
success: 1
file_date_updated: 2021-09-27T10:54:51Z
has_accepted_license: '1'
keyword:
- minimum 0-extension problem
- metric labeling problem
- discrete metric spaces
- metric extensions
- computational complexity
- valued constraint satisfaction problems
- discrete convex analysis
- L-convex functions
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2109.10203'
month: '09'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Generalized minimum 0-extension problem and discrete convexity
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_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
arxiv: 1
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
arxiv: 1
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: '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
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publication_identifier:
issn:
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publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
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title: 'Projection methods with alternating inertial steps for variational inequalities:
Weak and linear convergence'
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...
---
_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
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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
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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'
...