---
_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"
acknowledgement: We thank the anonymous reviewers for their careful reading of our
manuscript and their many insightful comments and suggestions. Open access funding
provided by Institute of Science and Technology (IST Austria).
article_number: '2109.10203'
article_processing_charge: Yes (via OA deal)
article_type: original
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. Mathematical Programming. 2024. doi:10.1007/s10107-024-02064-5
apa: Dvorak, M., & Kolmogorov, V. (2024). Generalized minimum 0-extension problem
and discrete convexity. Mathematical Programming. Springer Nature. https://doi.org/10.1007/s10107-024-02064-5
chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension
Problem and Discrete Convexity.” Mathematical Programming. Springer Nature,
2024. https://doi.org/10.1007/s10107-024-02064-5.
ieee: M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and
discrete convexity,” Mathematical Programming. Springer Nature, 2024.
ista: Dvorak M, Kolmogorov V. 2024. Generalized minimum 0-extension problem and
discrete convexity. Mathematical Programming., 2109.10203.
mla: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem
and Discrete Convexity.” Mathematical Programming, 2109.10203, Springer
Nature, 2024, doi:10.1007/s10107-024-02064-5.
short: M. Dvorak, V. Kolmogorov, Mathematical Programming (2024).
date_created: 2021-09-27T10:48:23Z
date_published: 2024-03-07T00:00:00Z
date_updated: 2024-03-19T08:20:31Z
day: '07'
ddc:
- '004'
department:
- _id: GradSch
- _id: VlKo
doi: 10.1007/s10107-024-02064-5
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
license: https://creativecommons.org/licenses/by/4.0/
month: '03'
oa: 1
oa_version: Preprint
publication: Mathematical Programming
publication_identifier:
eissn:
- 1436-4646
issn:
- 0025-5610
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalized minimum 0-extension problem and discrete convexity
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_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
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: '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
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: '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
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: '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
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
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
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file_date_updated: 2021-03-16T23:30:06Z
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intvolume: ' 101'
isi: 1
issue: '1'
language:
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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'
...