--- _id: '7577' abstract: - lang: eng text: Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods. acknowledgement: The project of the first author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola citation: ama: Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287 apa: Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287 chicago: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor & Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287. ieee: Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor & Francis, pp. 192–216, 2022. ista: Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216. mla: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor & Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287. short: Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216. date_created: 2020-03-09T07:06:52Z date_published: 2022-01-01T00:00:00Z date_updated: 2024-03-05T14:01:52Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1080/00036811.2020.1736287 ec_funded: 1 external_id: arxiv: - '2101.08057' isi: - '000518364100001' file: - access_level: open_access checksum: 869efe8cb09505dfa6012f67d20db63d content_type: application/pdf creator: dernst date_created: 2020-10-12T10:42:54Z date_updated: 2021-03-16T23:30:06Z embargo: 2021-03-15 file_id: '8648' file_name: 2020_ApplicAnalysis_Shehu.pdf file_size: 4282586 relation: main_file file_date_updated: 2021-03-16T23:30:06Z has_accepted_license: '1' intvolume: ' 101' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 192-216 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Applicable Analysis publication_identifier: eissn: - 1563-504X issn: - 0003-6811 publication_status: published publisher: Taylor & Francis quality_controlled: '1' scopus_import: '1' status: public title: Weak convergence for variational inequalities with inertial-type method type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 101 year: '2022' ... --- _id: '10072' abstract: - lang: eng text: The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works revealed that the LLL has intimate connections with a class of stochastic local search algorithms for finding such desirable objects. In particular, it can be seen as a sufficient condition for this type of algorithms to converge fast. Besides conditions for existence of and fast convergence to desirable objects, one may naturally ask further questions regarding properties of these algorithms. For instance, "are they parallelizable?", "how many solutions can they output?", "what is the expected "weight" of a solution?", etc. These questions and more have been answered for a class of LLL-inspired algorithms called commutative. In this paper we introduce a new, very natural and more general notion of commutativity (essentially matrix commutativity) which allows us to show a number of new refined properties of LLL-inspired local search algorithms with significantly simpler proofs. acknowledgement: "Fotis Iliopoulos: This material is based upon work directly supported by the IAS Fund for Math and indirectly supported by the National Science Foundation Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the National Science Foundation Grant No. CCF-1815328.\r\nVladimir Kolmogorov: Supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160." alternative_title: - LIPIcs article_number: '31' article_processing_charge: Yes author: - first_name: David G. full_name: Harris, David G. last_name: Harris - first_name: Fotis full_name: Iliopoulos, Fotis last_name: Iliopoulos - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the algorithmic Lovász Local Lemma. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Vol 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31' apa: 'Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2021). A new notion of commutativity for the algorithmic Lovász Local Lemma. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Vol. 207). Virtual: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31' chicago: Harris, David G., Fotis Iliopoulos, and Vladimir Kolmogorov. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Vol. 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31. ieee: D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity for the algorithmic Lovász Local Lemma,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Virtual, 2021, vol. 207. ista: 'Harris DG, Iliopoulos F, Kolmogorov V. 2021. A new notion of commutativity for the algorithmic Lovász Local Lemma. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation, LIPIcs, vol. 207, 31.' mla: Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic Lovász Local Lemma.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, vol. 207, 31, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31. short: D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. conference: end_date: 2021-08-18 location: Virtual name: 'APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/ Randomization and Computation' start_date: 2021-08-16 date_created: 2021-10-03T22:01:22Z date_published: 2021-09-15T00:00:00Z date_updated: 2022-03-18T10:08:25Z day: '15' ddc: - '000' department: - _id: VlKo doi: 10.4230/LIPIcs.APPROX/RANDOM.2021.31 ec_funded: 1 external_id: arxiv: - '2008.05569' file: - access_level: open_access checksum: 9d2544d53aa5b01565c6891d97a4d765 content_type: application/pdf creator: cchlebak date_created: 2021-10-06T13:51:54Z date_updated: 2021-10-06T13:51:54Z file_id: '10098' file_name: 2021_LIPIcs_Harris.pdf file_size: 804472 relation: main_file success: 1 file_date_updated: 2021-10-06T13:51:54Z has_accepted_license: '1' intvolume: ' 207' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques publication_identifier: isbn: - 978-3-9597-7207-5 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: A new notion of commutativity for the algorithmic Lovász Local Lemma tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 207 year: '2021' ... --- _id: '10552' abstract: - lang: eng text: We study a class of convex-concave saddle-point problems of the form minxmaxy⟨Kx,y⟩+fP(x)−h∗(y) where K is a linear operator, fP is the sum of a convex function f with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope P, and h∗ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle (lmo) for fP and an efficient proximal map for h∗ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case h∗ is the indicator function of a linear constraint and function f is quadratic, we show a O(1/n2) convergence rate on the dual objective, requiring O(nlogn) calls of lmo. If the problem comes from the constrained optimization problem minx∈Rd{fP(x)|Ax−b=0} then we additionally get bound O(1/n2) both on the primal gap and on the infeasibility gap. In the most general case, we show a O(1/n) convergence rate of the primal-dual gap again requiring O(nlogn) calls of lmo. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision. acknowledgement: Vladimir Kolmogorov was supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160. Thomas Pock acknowledges support by an ERC grant HOMOVIS, no 640156. article_processing_charge: No author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Thomas full_name: Pock, Thomas last_name: Pock citation: ama: 'Kolmogorov V, Pock T. One-sided Frank-Wolfe algorithms for saddle problems. In: 38th International Conference on Machine Learning. ; 2021.' apa: Kolmogorov, V., & Pock, T. (2021). One-sided Frank-Wolfe algorithms for saddle problems. In 38th International Conference on Machine Learning. Virtual. chicago: Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” In 38th International Conference on Machine Learning, 2021. ieee: V. Kolmogorov and T. Pock, “One-sided Frank-Wolfe algorithms for saddle problems,” in 38th International Conference on Machine Learning, Virtual, 2021. ista: 'Kolmogorov V, Pock T. 2021. One-sided Frank-Wolfe algorithms for saddle problems. 38th International Conference on Machine Learning. ICML: International Conference on Machine Learning.' mla: Kolmogorov, Vladimir, and Thomas Pock. “One-Sided Frank-Wolfe Algorithms for Saddle Problems.” 38th International Conference on Machine Learning, 2021. short: V. Kolmogorov, T. Pock, in:, 38th International Conference on Machine Learning, 2021. conference: end_date: 2021-07-24 location: Virtual name: 'ICML: International Conference on Machine Learning' start_date: 2021-07-18 date_created: 2021-12-16T12:41:20Z date_published: 2021-07-01T00:00:00Z date_updated: 2021-12-17T09:06:46Z day: '01' department: - _id: VlKo ec_funded: 1 external_id: arxiv: - '2101.12617' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.12617 month: '07' oa: 1 oa_version: Preprint project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: 38th International Conference on Machine Learning publication_status: published quality_controlled: '1' status: public title: One-sided Frank-Wolfe algorithms for saddle problems type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2021' ... --- _id: '9592' abstract: - lang: eng text: The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large odd-sized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large even-sized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general. article_processing_charge: No author: - first_name: Martin full_name: Dvorak, Martin id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425 last_name: Dvorak orcid: 0000-0001-5293-214X - first_name: Sara full_name: Nicholson, Sara last_name: Nicholson citation: ama: 'Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. In: Proceedings of the 33rd Canadian Conference on Computational Geometry.' apa: Dvorak, M., & Nicholson, S. (n.d.). Massively winning configurations in the convex grabbing game on the plane. In Proceedings of the 33rd Canadian Conference on Computational Geometry. Halifax, NS, Canada. chicago: Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” In Proceedings of the 33rd Canadian Conference on Computational Geometry, n.d. ieee: M. Dvorak and S. Nicholson, “Massively winning configurations in the convex grabbing game on the plane,” in Proceedings of the 33rd Canadian Conference on Computational Geometry, Halifax, NS, Canada. ista: 'Dvorak M, Nicholson S. Massively winning configurations in the convex grabbing game on the plane. Proceedings of the 33rd Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry.' mla: Dvorak, Martin, and Sara Nicholson. “Massively Winning Configurations in the Convex Grabbing Game on the Plane.” Proceedings of the 33rd Canadian Conference on Computational Geometry. short: M. Dvorak, S. Nicholson, in:, Proceedings of the 33rd Canadian Conference on Computational Geometry, n.d. conference: end_date: 2021-08-12 location: Halifax, NS, Canada name: 'CCCG: Canadian Conference on Computational Geometry' start_date: 2021-08-10 date_created: 2021-06-22T15:57:11Z date_published: 2021-06-29T00:00:00Z date_updated: 2021-08-12T10:57:39Z day: '29' ddc: - '516' department: - _id: GradSch - _id: VlKo external_id: arxiv: - '2106.11247' file: - access_level: open_access checksum: 45accb1de9b7e0e4bb2fbfe5fd3e6239 content_type: application/pdf creator: mdvorak date_created: 2021-06-28T20:23:13Z date_updated: 2021-06-28T20:23:13Z file_id: '9616' file_name: Convex-Grabbing-Game_CCCG_proc_version.pdf file_size: 381306 relation: main_file success: 1 - access_level: open_access checksum: 9199cf18c65658553487458cc24d0ab2 content_type: application/pdf creator: kschuh date_created: 2021-08-12T10:57:21Z date_updated: 2021-08-12T10:57:21Z file_id: '9902' file_name: Convex-Grabbing-Game_FULL-VERSION.pdf file_size: 403645 relation: main_file success: 1 file_date_updated: 2021-08-12T10:57:21Z has_accepted_license: '1' keyword: - convex grabbing game - graph grabbing game - combinatorial game - convex geometry language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '06' oa: 1 oa_version: Submitted Version publication: Proceedings of the 33rd Canadian Conference on Computational Geometry publication_status: accepted quality_controlled: '1' status: public title: Massively winning configurations in the convex grabbing game on the plane tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '9469' abstract: - lang: eng text: In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis. acknowledgement: The authors are grateful to the anonymous referees and the handling Editor for their insightful comments which have improved the earlier version of the manuscript greatly. The second author is grateful to the University of Hafr Al Batin. The last author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Cyril D. full_name: Enyi, Cyril D. last_name: Enyi - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 2021. doi:10.1080/10556788.2021.1924715 apa: Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2021). Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. Taylor and Francis. https://doi.org/10.1080/10556788.2021.1924715 chicago: Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software. Taylor and Francis, 2021. https://doi.org/10.1080/10556788.2021.1924715. ieee: O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” Optimization Methods and Software. Taylor and Francis, 2021. ista: Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. mla: Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software, Taylor and Francis, 2021, doi:10.1080/10556788.2021.1924715. short: O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software (2021). date_created: 2021-06-06T22:01:30Z date_published: 2021-05-12T00:00:00Z date_updated: 2023-08-08T13:57:43Z day: '12' department: - _id: VlKo doi: 10.1080/10556788.2021.1924715 ec_funded: 1 external_id: isi: - '000650507600001' isi: 1 language: - iso: eng month: '05' oa_version: None project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Optimization Methods and Software publication_identifier: eissn: - 1029-4937 issn: - 1055-6788 publication_status: published publisher: Taylor and Francis quality_controlled: '1' scopus_import: '1' status: public title: Reflected three-operator splitting method for monotone inclusion problem type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _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: '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: '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: '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: '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: '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: - '000537342300001' file: - access_level: open_access checksum: 63c5f31cd04626152a19f97a2476281b content_type: application/pdf creator: kschuh date_created: 2024-03-07T14:58:51Z date_updated: 2024-03-07T14:58:51Z file_id: '15089' file_name: 2021_OptimizationLetters_Shehu.pdf file_size: 2148882 relation: main_file success: 1 file_date_updated: 2024-03-07T14:58:51Z has_accepted_license: '1' intvolume: ' 15' isi: 1 language: - iso: eng 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: '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 day: '01' ddc: - '000' department: - _id: VlKo doi: 10.1007/s11075-019-00758-y ec_funded: 1 external_id: isi: - '000528979000015' file: - access_level: open_access checksum: bb1a1eb3ebb2df380863d0db594673ba content_type: application/pdf creator: kschuh date_created: 2019-10-01T13:14:10Z date_updated: 2020-07-14T12:47:34Z file_id: '6927' file_name: ExtragradientMethodPaper.pdf file_size: 359654 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 84' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Submitted Version page: 365-388 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 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' ... --- _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 day: '01' ddc: - '510' department: - _id: VlKo doi: 10.1016/j.apnum.2020.06.009 ec_funded: 1 external_id: isi: - '000564648400018' file: - access_level: open_access checksum: 87d81324a62c82baa925c009dfcb0200 content_type: application/pdf creator: dernst date_created: 2020-07-02T09:08:59Z date_updated: 2020-07-14T12:48:09Z file_id: '8078' file_name: 2020_AppliedNumericalMath_Shehu.pdf file_size: 2874203 relation: main_file file_date_updated: 2020-07-14T12:48:09Z has_accepted_license: '1' intvolume: ' 157' isi: 1 language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 315-337 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Applied Numerical Mathematics publication_identifier: issn: - 0168-9274 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: 'Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 157 year: '2020' ... --- _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 day: '01' ddc: - '518' - '510' - '515' department: - _id: VlKo doi: 10.1007/s10957-019-01616-6 ec_funded: 1 external_id: isi: - '000511805200009' file: - access_level: open_access checksum: 9f6dc6c6bf2b48cb3a2091a9ed5feaf2 content_type: application/pdf creator: dernst date_created: 2020-10-12T10:40:27Z date_updated: 2021-03-16T23:30:04Z embargo: 2021-03-15 file_id: '8647' file_name: 2020_JourOptimizationTheoryApplic_Shehu.pdf file_size: 332641 relation: main_file file_date_updated: 2021-03-16T23:30:04Z has_accepted_license: '1' intvolume: ' 184' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 877–894 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 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: '6725' abstract: - lang: eng text: "A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language. \r\nRecent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds." alternative_title: - LIPIcs author: - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Kolmogorov V. Testing the complexity of a valued CSP language. In: 46th International Colloquium on Automata, Languages and Programming. Vol 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:77:1-77:12. doi:10.4230/LIPICS.ICALP.2019.77' apa: 'Kolmogorov, V. (2019). Testing the complexity of a valued CSP language. In 46th International Colloquium on Automata, Languages and Programming (Vol. 132, p. 77:1-77:12). Patras, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ICALP.2019.77' chicago: Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” In 46th International Colloquium on Automata, Languages and Programming, 132:77:1-77:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.ICALP.2019.77. ieee: V. Kolmogorov, “Testing the complexity of a valued CSP language,” in 46th International Colloquium on Automata, Languages and Programming, Patras, Greece, 2019, vol. 132, p. 77:1-77:12. ista: 'Kolmogorov V. 2019. Testing the complexity of a valued CSP language. 46th International Colloquium on Automata, Languages and Programming. ICALP 2019: International Colloquim on Automata, Languages and Programming, LIPIcs, vol. 132, 77:1-77:12.' mla: Kolmogorov, Vladimir. “Testing the Complexity of a Valued CSP Language.” 46th International Colloquium on Automata, Languages and Programming, vol. 132, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12, doi:10.4230/LIPICS.ICALP.2019.77. short: V. Kolmogorov, in:, 46th International Colloquium on Automata, Languages and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 77:1-77:12. conference: end_date: 2019-07-12 location: Patras, Greece name: 'ICALP 2019: International Colloquim on Automata, Languages and Programming' start_date: 2019-07-08 date_created: 2019-07-29T12:23:29Z date_published: 2019-07-01T00:00:00Z date_updated: 2021-01-12T08:08:40Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.4230/LIPICS.ICALP.2019.77 ec_funded: 1 external_id: arxiv: - '1803.02289' file: - access_level: open_access checksum: f5ebee8eec6ae09e30365578ee63a492 content_type: application/pdf creator: dernst date_created: 2019-07-31T07:01:45Z date_updated: 2020-07-14T12:47:38Z file_id: '6738' file_name: 2019_LIPICS_Kolmogorov.pdf file_size: 575475 relation: main_file file_date_updated: 2020-07-14T12:47:38Z has_accepted_license: '1' intvolume: ' 132' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 77:1-77:12 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: 46th International Colloquium on Automata, Languages and Programming publication_identifier: isbn: - 978-3-95977-109-2 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Testing the complexity of a valued CSP language 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: 132 year: '2019' ... --- _id: '6596' abstract: - lang: eng text: It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper. article_number: '138' 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 citation: ama: Shehu Y. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 2019;74(4). doi:10.1007/s00025-019-1061-4 apa: Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. Springer. https://doi.org/10.1007/s00025-019-1061-4 chicago: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics. Springer, 2019. https://doi.org/10.1007/s00025-019-1061-4. ieee: Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces,” Results in Mathematics, vol. 74, no. 4. Springer, 2019. ista: Shehu Y. 2019. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138. mla: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics, vol. 74, no. 4, 138, Springer, 2019, doi:10.1007/s00025-019-1061-4. short: Y. Shehu, Results in Mathematics 74 (2019). date_created: 2019-06-29T10:11:30Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-08-28T12:26:22Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.1007/s00025-019-1061-4 ec_funded: 1 external_id: arxiv: - '2101.09068' isi: - '000473237500002' file: - access_level: open_access checksum: c6d18cb1e16fc0c36a0e0f30b4ebbc2d content_type: application/pdf creator: kschuh date_created: 2019-07-03T15:20:40Z date_updated: 2020-07-14T12:47:34Z file_id: '6605' file_name: Springer_2019_Shehu.pdf file_size: 466942 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 74' isi: 1 issue: '4' language: - iso: eng month: '12' 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' - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Results in Mathematics publication_identifier: eissn: - 1420-9012 issn: - 1422-6383 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 74 year: '2019' ... --- _id: '7000' abstract: - lang: eng text: The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps. article_number: '161' 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: 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, Iyiola OS, Li X-H, Dong Q-L. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 2019;38(4). doi:10.1007/s40314-019-0955-9 apa: Shehu, Y., Iyiola, O. S., Li, X.-H., & Dong, Q.-L. (2019). Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. Springer Nature. https://doi.org/10.1007/s40314-019-0955-9 chicago: Shehu, Yekini, Olaniyi S. Iyiola, Xiao-Huan Li, and Qiao-Li Dong. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics. Springer Nature, 2019. https://doi.org/10.1007/s40314-019-0955-9. ieee: Y. Shehu, O. S. Iyiola, X.-H. Li, and Q.-L. Dong, “Convergence analysis of projection method for variational inequalities,” Computational and Applied Mathematics, vol. 38, no. 4. Springer Nature, 2019. ista: Shehu Y, Iyiola OS, Li X-H, Dong Q-L. 2019. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 38(4), 161. mla: Shehu, Yekini, et al. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics, vol. 38, no. 4, 161, Springer Nature, 2019, doi:10.1007/s40314-019-0955-9. short: Y. Shehu, O.S. Iyiola, X.-H. Li, Q.-L. Dong, Computational and Applied Mathematics 38 (2019). date_created: 2019-11-12T12:41:44Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-08-30T07:20:32Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1007/s40314-019-0955-9 ec_funded: 1 external_id: arxiv: - '2101.09081' isi: - '000488973100005' has_accepted_license: '1' intvolume: ' 38' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s40314-019-0955-9 month: '12' 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: Computational and Applied Mathematics publication_identifier: eissn: - 1807-0302 issn: - 2238-3603 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Convergence analysis of projection method for variational inequalities type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 38 year: '2019' ... --- _id: '7412' abstract: - lang: eng text: We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These algorithms search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a random nearby state that addresses the violation, while (we hope) not introducing many new violations. An important class of focused local search algorithms with provable performance guarantees has recently arisen from algorithmizations of the Lovász local lemma (LLL), a nonconstructive tool for proving the existence of satisfying states by introducing a background measure on the state space. While powerful, the state transitions of algorithms in this class must be, in a precise sense, perfectly compatible with the background measure. In many applications this is a very restrictive requirement, and one needs to step outside the class. Here we introduce the notion of measure distortion and develop a framework for analyzing arbitrary focused stochastic local search algorithms, recovering LLL algorithmizations as the special case of no distortion. Our framework takes as input an arbitrary algorithm of such type and an arbitrary probability measure and shows how to use the measure as a yardstick of algorithmic progress, even for algorithms designed independently of the measure. article_processing_charge: No article_type: original author: - first_name: Dimitris full_name: Achlioptas, Dimitris last_name: Achlioptas - 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: Achlioptas D, Iliopoulos F, Kolmogorov V. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 2019;48(5):1583-1602. doi:10.1137/16m109332x apa: Achlioptas, D., Iliopoulos, F., & Kolmogorov, V. (2019). A local lemma for focused stochastical algorithms. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/16m109332x chicago: Achlioptas, Dimitris, Fotis Iliopoulos, and Vladimir Kolmogorov. “A Local Lemma for Focused Stochastical Algorithms.” SIAM Journal on Computing. SIAM, 2019. https://doi.org/10.1137/16m109332x. ieee: D. Achlioptas, F. Iliopoulos, and V. Kolmogorov, “A local lemma for focused stochastical algorithms,” SIAM Journal on Computing, vol. 48, no. 5. SIAM, pp. 1583–1602, 2019. ista: Achlioptas D, Iliopoulos F, Kolmogorov V. 2019. A local lemma for focused stochastical algorithms. SIAM Journal on Computing. 48(5), 1583–1602. mla: Achlioptas, Dimitris, et al. “A Local Lemma for Focused Stochastical Algorithms.” SIAM Journal on Computing, vol. 48, no. 5, SIAM, 2019, pp. 1583–602, doi:10.1137/16m109332x. short: D. Achlioptas, F. Iliopoulos, V. Kolmogorov, SIAM Journal on Computing 48 (2019) 1583–1602. date_created: 2020-01-30T09:27:32Z date_published: 2019-10-31T00:00:00Z date_updated: 2023-09-06T15:25:29Z day: '31' department: - _id: VlKo doi: 10.1137/16m109332x ec_funded: 1 external_id: arxiv: - '1809.01537' isi: - '000493900200005' intvolume: ' 48' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1809.01537 month: '10' oa: 1 oa_version: Preprint page: 1583-1602 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: SIAM quality_controlled: '1' scopus_import: '1' status: public title: A local lemma for focused stochastical algorithms type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 48 year: '2019' ... --- _id: '7468' abstract: - lang: eng text: We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane block-coordinate Frank-Wolfe method that takes advantage of the specific structure of the Lagrangean decomposition. We show empirically that our method outperforms state-of-the-art Lagrangean decomposition based algorithms on some challenging Markov Random Field, multi-label discrete tomography and graph matching problems. article_number: 11138-11147 article_processing_charge: No author: - first_name: Paul full_name: Swoboda, Paul id: 446560C6-F248-11E8-B48F-1D18A9856A87 last_name: Swoboda - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov citation: ama: 'Swoboda P, Kolmogorov V. Map inference via block-coordinate Frank-Wolfe algorithm. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol 2019-June. IEEE; 2019. doi:10.1109/CVPR.2019.01140' apa: 'Swoboda, P., & Kolmogorov, V. (2019). Map inference via block-coordinate Frank-Wolfe algorithm. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Vol. 2019–June). Long Beach, CA, United States: IEEE. https://doi.org/10.1109/CVPR.2019.01140' chicago: Swoboda, Paul, and Vladimir Kolmogorov. “Map Inference via Block-Coordinate Frank-Wolfe Algorithm.” In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2019–June. IEEE, 2019. https://doi.org/10.1109/CVPR.2019.01140. ieee: P. Swoboda and V. Kolmogorov, “Map inference via block-coordinate Frank-Wolfe algorithm,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Long Beach, CA, United States, 2019, vol. 2019–June. ista: 'Swoboda P, Kolmogorov V. 2019. Map inference via block-coordinate Frank-Wolfe algorithm. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition vol. 2019–June, 11138–11147.' mla: Swoboda, Paul, and Vladimir Kolmogorov. “Map Inference via Block-Coordinate Frank-Wolfe Algorithm.” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2019–June, 11138–11147, IEEE, 2019, doi:10.1109/CVPR.2019.01140. short: P. Swoboda, V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2019. conference: end_date: 2019-06-20 location: Long Beach, CA, United States name: 'CVPR: Conference on Computer Vision and Pattern Recognition' start_date: 2019-06-15 date_created: 2020-02-09T23:00:52Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-07T14:54:24Z day: '01' department: - _id: VlKo doi: 10.1109/CVPR.2019.01140 ec_funded: 1 external_id: arxiv: - '1806.05049' isi: - '000542649304076' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1806.05049 month: '06' 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: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition publication_identifier: isbn: - '9781728132938' issn: - '10636919' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: Map inference via block-coordinate Frank-Wolfe algorithm type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 2019-June year: '2019' ...