--- _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' ...