[{"article_processing_charge":"No","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2022-01-01T00:00:00Z","page":"192-216","article_type":"original","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","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.","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","ista":"Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216.","short":"Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 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.","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."},"publication":"Applicable Analysis","issue":"1","abstract":[{"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.","lang":"eng"}],"type":"journal_article","file":[{"relation":"main_file","file_id":"8648","embargo":"2021-03-15","date_updated":"2021-03-16T23:30:06Z","date_created":"2020-10-12T10:42:54Z","checksum":"869efe8cb09505dfa6012f67d20db63d","file_name":"2020_ApplicAnalysis_Shehu.pdf","access_level":"open_access","file_size":4282586,"content_type":"application/pdf","creator":"dernst"}],"oa_version":"Submitted Version","intvolume":" 101","status":"public","title":"Weak convergence for variational inequalities with inertial-type method","ddc":["510","515","518"],"_id":"7577","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0003-6811"],"eissn":["1563-504X"]},"month":"01","language":[{"iso":"eng"}],"doi":"10.1080/00036811.2020.1736287","project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000518364100001"],"arxiv":["2101.08057"]},"oa":1,"ec_funded":1,"file_date_updated":"2021-03-16T23:30:06Z","volume":101,"date_updated":"2024-03-05T14:01:52Z","date_created":"2020-03-09T07:06:52Z","author":[{"full_name":"Shehu, Yekini","last_name":"Shehu","first_name":"Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S.","last_name":"Iyiola"}],"department":[{"_id":"VlKo"}],"publisher":"Taylor & Francis","publication_status":"published","year":"2022","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)."},{"department":[{"_id":"VlKo"}],"publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","publication_status":"published","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.","year":"2021","volume":207,"date_created":"2021-10-03T22:01:22Z","date_updated":"2022-03-18T10:08:25Z","author":[{"full_name":"Harris, David G.","first_name":"David G.","last_name":"Harris"},{"last_name":"Iliopoulos","first_name":"Fotis","full_name":"Iliopoulos, Fotis"},{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov"}],"article_number":"31","license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"file_date_updated":"2021-10-06T13:51:54Z","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["2008.05569"]},"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.APPROX/RANDOM.2021.31","conference":{"end_date":"2021-08-18","location":"Virtual","start_date":"2021-08-16","name":"APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation"},"publication_identifier":{"isbn":["978-3-9597-7207-5"],"issn":["1868-8969"]},"month":"09","intvolume":" 207","title":"A new notion of commutativity for the algorithmic Lovász Local Lemma","ddc":["000"],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10072","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"10098","checksum":"9d2544d53aa5b01565c6891d97a4d765","success":1,"date_updated":"2021-10-06T13:51:54Z","date_created":"2021-10-06T13:51:54Z","access_level":"open_access","file_name":"2021_LIPIcs_Harris.pdf","file_size":804472,"content_type":"application/pdf","creator":"cchlebak"}],"alternative_title":["LIPIcs"],"type":"conference","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."}],"citation":{"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.","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","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.","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","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.","short":"D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","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."},"publication":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques","date_published":"2021-09-15T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes","has_accepted_license":"1","day":"15"},{"type":"conference","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."}],"ec_funded":1,"publication_status":"published","title":"One-sided Frank-Wolfe algorithms for saddle problems","status":"public","department":[{"_id":"VlKo"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"10552","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.","year":"2021","date_created":"2021-12-16T12:41:20Z","date_updated":"2021-12-17T09:06:46Z","oa_version":"Preprint","author":[{"last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir"},{"full_name":"Pock, Thomas","last_name":"Pock","first_name":"Thomas"}],"day":"01","month":"07","article_processing_charge":"No","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"}],"publication":"38th International Conference on Machine Learning","main_file_link":[{"url":"https://arxiv.org/abs/2101.12617","open_access":"1"}],"citation":{"ieee":"V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,” in 38th International Conference on Machine Learning, Virtual, 2021.","apa":"Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for saddle problems. In 38th International Conference on Machine Learning. Virtual.","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.","ama":"Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems. In: 38th International Conference on Machine Learning. ; 2021.","chicago":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” In 38th International Conference on Machine Learning, 2021.","short":"V. Kolmogorov, T. Pock, in:, 38th International Conference on Machine Learning, 2021.","mla":"Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” 38th International Conference on Machine Learning, 2021."},"external_id":{"arxiv":["2101.12617"]},"oa":1,"language":[{"iso":"eng"}],"conference":{"end_date":"2021-07-24","start_date":"2021-07-18","location":"Virtual","name":"ICML: International Conference on Machine Learning"},"date_published":"2021-07-01T00:00:00Z"},{"day":"29","article_processing_charge":"No","has_accepted_license":"1","keyword":["convex grabbing game","graph grabbing game","combinatorial game","convex geometry"],"date_published":"2021-06-29T00:00:00Z","publication":"Proceedings of the 33rd Canadian Conference on Computational Geometry","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.","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.","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.","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.","short":"M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference on Computational Geometry, n.d.","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.","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."},"abstract":[{"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.","lang":"eng"}],"type":"conference","file":[{"access_level":"open_access","file_name":"Convex-Grabbing-Game_CCCG_proc_version.pdf","creator":"mdvorak","content_type":"application/pdf","file_size":381306,"file_id":"9616","relation":"main_file","success":1,"checksum":"45accb1de9b7e0e4bb2fbfe5fd3e6239","date_updated":"2021-06-28T20:23:13Z","date_created":"2021-06-28T20:23:13Z"},{"file_id":"9902","relation":"main_file","success":1,"checksum":"9199cf18c65658553487458cc24d0ab2","date_updated":"2021-08-12T10:57:21Z","date_created":"2021-08-12T10:57:21Z","access_level":"open_access","file_name":"Convex-Grabbing-Game_FULL-VERSION.pdf","creator":"kschuh","content_type":"application/pdf","file_size":403645}],"oa_version":"Submitted Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"9592","status":"public","title":"Massively winning configurations in the convex grabbing game on the plane","ddc":["516"],"month":"06","conference":{"end_date":"2021-08-12","start_date":"2021-08-10","location":"Halifax, NS, Canada","name":"CCCG: Canadian Conference on Computational Geometry"},"language":[{"iso":"eng"}],"tmp":{"short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"oa":1,"external_id":{"arxiv":["2106.11247"]},"quality_controlled":"1","file_date_updated":"2021-08-12T10:57:21Z","license":"https://creativecommons.org/licenses/by-nd/4.0/","author":[{"id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","orcid":"0000-0001-5293-214X","first_name":"Martin","last_name":"Dvorak","full_name":"Dvorak, Martin"},{"first_name":"Sara","last_name":"Nicholson","full_name":"Nicholson, Sara"}],"date_updated":"2021-08-12T10:57:39Z","date_created":"2021-06-22T15:57:11Z","year":"2021","publication_status":"accepted","department":[{"_id":"GradSch"},{"_id":"VlKo"}]},{"date_updated":"2023-08-08T13:57:43Z","date_created":"2021-06-06T22:01:30Z","author":[{"full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola","first_name":"Olaniyi S."},{"last_name":"Enyi","first_name":"Cyril D.","full_name":"Enyi, Cyril D."},{"first_name":"Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini"}],"department":[{"_id":"VlKo"}],"publisher":"Taylor and Francis","publication_status":"published","year":"2021","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).","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1080/10556788.2021.1924715","project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000650507600001"]},"publication_identifier":{"eissn":["1029-4937"],"issn":["1055-6788"]},"month":"05","oa_version":"None","status":"public","title":"Reflected three-operator splitting method for monotone inclusion problem","_id":"9469","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"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.","lang":"eng"}],"type":"journal_article","date_published":"2021-05-12T00:00:00Z","article_type":"original","citation":{"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.","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).","ista":"Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software.","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.","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","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"},"publication":"Optimization Methods and Software","article_processing_charge":"No","day":"12","scopus_import":"1"}]