--- _id: '7577' abstract: - lang: eng text: Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods. acknowledgement: The project of the first author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola citation: ama: Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287 apa: Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287 chicago: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor & Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287. ieee: Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor & Francis, pp. 192–216, 2022. ista: Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216. mla: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor & Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287. short: Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216. date_created: 2020-03-09T07:06:52Z date_published: 2022-01-01T00:00:00Z date_updated: 2024-03-05T14:01:52Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1080/00036811.2020.1736287 ec_funded: 1 external_id: arxiv: - '2101.08057' isi: - '000518364100001' file: - access_level: open_access checksum: 869efe8cb09505dfa6012f67d20db63d content_type: application/pdf creator: dernst date_created: 2020-10-12T10:42:54Z date_updated: 2021-03-16T23:30:06Z embargo: 2021-03-15 file_id: '8648' file_name: 2020_ApplicAnalysis_Shehu.pdf file_size: 4282586 relation: main_file file_date_updated: 2021-03-16T23:30:06Z has_accepted_license: '1' intvolume: ' 101' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 192-216 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Applicable Analysis publication_identifier: eissn: - 1563-504X issn: - 0003-6811 publication_status: published publisher: Taylor & Francis quality_controlled: '1' scopus_import: '1' status: public title: Weak convergence for variational inequalities with inertial-type method type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 101 year: '2022' ... --- _id: '10072' abstract: - lang: eng text: The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works revealed that the LLL has intimate connections with a class of stochastic local search algorithms for finding such desirable objects. In particular, it can be seen as a sufficient condition for this type of algorithms to converge fast. Besides conditions for existence of and fast convergence to desirable objects, one may naturally ask further questions regarding properties of these algorithms. For instance, "are they parallelizable?", "how many solutions can they output?", "what is the expected "weight" of a solution?", etc. These questions and more have been answered for a class of LLL-inspired algorithms called commutative. In this paper we introduce a new, very natural and more general notion of commutativity (essentially matrix commutativity) which allows us to show a number of new refined properties of LLL-inspired local search algorithms with significantly simpler proofs. acknowledgement: "Fotis Iliopoulos: This material is based upon work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the National Science Foundation Grant No. CCF-1815328.\r\nVladimir Kolmogorov: Supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160." alternative_title: - LIPIcs article_number: '31' article_processing_charge: Yes author: - first_name: David G. full_name: Harris, David G. last_name: Harris - first_name: Fotis full_name: Iliopoulos, Fotis last_name: Iliopoulos - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the algorithmic Lovász Local Lemma. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Vol 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31' apa: 'Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2021). A new notion of commutativity for the algorithmic Lovász Local Lemma. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Vol. 207). Virtual: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31' chicago: Harris, David G., Fotis Iliopoulos, and Vladimir Kolmogorov. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Vol. 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31. ieee: D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity for the algorithmic Lovász Local Lemma,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Virtual, 2021, vol. 207. ista: 'Harris DG, Iliopoulos F, Kolmogorov V. 2021. A new notion of commutativity for the algorithmic Lovász Local Lemma. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation, LIPIcs, vol. 207, 31.' mla: Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, vol. 207, 31, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31. short: D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. conference: end_date: 2021-08-18 location: Virtual name: 'APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation' start_date: 2021-08-16 date_created: 2021-10-03T22:01:22Z date_published: 2021-09-15T00:00:00Z date_updated: 2022-03-18T10:08:25Z day: '15' ddc: - '000' department: - _id: VlKo doi: 10.4230/LIPIcs.APPROX/RANDOM.2021.31 ec_funded: 1 external_id: arxiv: - '2008.05569' file: - access_level: open_access checksum: 9d2544d53aa5b01565c6891d97a4d765 content_type: application/pdf creator: cchlebak date_created: 2021-10-06T13:51:54Z date_updated: 2021-10-06T13:51:54Z file_id: '10098' file_name: 2021_LIPIcs_Harris.pdf file_size: 804472 relation: main_file success: 1 file_date_updated: 2021-10-06T13:51:54Z has_accepted_license: '1' intvolume: ' 207' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ 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' ...