[{"license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2021-08-11T12:44:16Z","ec_funded":1,"publication_status":"published","department":[{"_id":"VlKo"}],"publisher":"Springer Nature","year":"2021","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).","date_created":"2021-03-10T12:18:47Z","date_updated":"2023-09-05T15:32:32Z","volume":21,"author":[{"last_name":"Izuchukwu","first_name":"Chinedu","full_name":"Izuchukwu, Chinedu"},{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini"}],"month":"06","publication_identifier":{"issn":["1566-113X"],"eissn":["1572-9427"]},"quality_controlled":"1","isi":1,"project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000625002100001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s11067-021-09517-w","type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"2","title":"New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity","status":"public","ddc":["510"],"intvolume":" 21","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"9234","file":[{"date_updated":"2021-08-11T12:44:16Z","date_created":"2021-08-11T12:44:16Z","checksum":"22b4253a2e5da843622a2df713784b4c","success":1,"relation":"main_file","file_id":"9884","content_type":"application/pdf","file_size":834964,"creator":"kschuh","file_name":"2021_NetworksSpatialEconomics_Shehu.pdf","access_level":"open_access"}],"oa_version":"Published Version","keyword":["Computer Networks and Communications","Software","Artificial Intelligence"],"scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","page":"291-323","publication":"Networks and Spatial Economics","citation":{"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.","short":"C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 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.","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.","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","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.","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"},"date_published":"2021-06-01T00:00:00Z"},{"oa_version":"None","volume":12601,"date_created":"2021-03-07T23:01:25Z","date_updated":"2023-10-10T09:29:08Z","author":[{"full_name":"Bloch-Hansen, Andrew","last_name":"Bloch-Hansen","first_name":"Andrew"},{"full_name":"Samei, Nasim","id":"C1531CAE-36E9-11EA-845F-33AA3DDC885E","first_name":"Nasim","last_name":"Samei"},{"full_name":"Solis-Oba, Roberto","first_name":"Roberto","last_name":"Solis-Oba"}],"publisher":"Springer Nature","intvolume":" 12601","department":[{"_id":"VlKo"}],"title":"Experimental evaluation of a local search approximation algorithm for the multiway cut problem","status":"public","publication_status":"published","_id":"9227","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"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.","lang":"eng"}],"alternative_title":["LNCS"],"type":"conference","language":[{"iso":"eng"}],"date_published":"2021-01-28T00:00:00Z","doi":"10.1007/978-3-030-67899-9_28","conference":{"location":"Rupnagar, India","start_date":"2021-02-11","end_date":"2021-02-13","name":"CALDAM: Conference on Algorithms and Discrete Applied Mathematics"},"page":"346-358","quality_controlled":"1","citation":{"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.","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.","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","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","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.","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."},"publication":"Conference on Algorithms and Discrete Applied Mathematics","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030678982"],"issn":["0302-9743"]},"article_processing_charge":"No","month":"01","day":"28","scopus_import":"1"},{"month":"04","publication_identifier":{"issn":["1432-2994"],"eissn":["1432-5217"]},"doi":"10.1007/s00186-020-00730-w","language":[{"iso":"eng"}],"external_id":{"isi":["000590497300001"]},"isi":1,"quality_controlled":"1","project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"}],"ec_funded":1,"author":[{"full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","first_name":"Yekini","last_name":"Shehu"},{"first_name":"Olaniyi S.","last_name":"Iyiola","full_name":"Iyiola, Olaniyi S."},{"full_name":"Thong, Duong Viet","last_name":"Thong","first_name":"Duong Viet"},{"first_name":"Nguyen Thi Cam","last_name":"Van","full_name":"Van, Nguyen Thi Cam"}],"date_updated":"2023-10-10T09:30:23Z","date_created":"2020-11-29T23:01:18Z","volume":93,"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).","year":"2021","publication_status":"published","department":[{"_id":"VlKo"}],"publisher":"Springer Nature","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2021-04-01T00:00:00Z","publication":"Mathematical Methods of Operations Research","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","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.","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","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.","short":"Y. Shehu, O.S. Iyiola, D.V. Thong, N.T.C. Van, Mathematical Methods of Operations Research 93 (2021) 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.","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."},"article_type":"original","page":"213-242","abstract":[{"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.","lang":"eng"}],"issue":"2","type":"journal_article","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8817","title":"An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems","status":"public","intvolume":" 93"},{"month":"03","publication_identifier":{"issn":["1422-6383"],"eissn":["1420-9012"]},"external_id":{"isi":["000632917700001"]},"quality_controlled":"1","isi":1,"doi":"10.1007/s00025-021-01381-x","language":[{"iso":"eng"}],"article_number":"75","year":"2021","acknowledgement":"The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"VlKo"}],"author":[{"full_name":"Iyiola, Olaniyi S.","first_name":"Olaniyi S.","last_name":"Iyiola"},{"orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini","full_name":"Shehu, Yekini"}],"date_created":"2021-04-11T22:01:14Z","date_updated":"2023-10-10T09:47:33Z","volume":76,"scopus_import":"1","day":"25","article_processing_charge":"No","publication":"Results in Mathematics","citation":{"short":"O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021).","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.","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.","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","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."},"article_type":"original","date_published":"2021-03-25T00:00:00Z","type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"2","_id":"9315","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications","intvolume":" 76","oa_version":"None"},{"doi":"10.1080/02331934.2021.1914035","language":[{"iso":"eng"}],"external_id":{"isi":["000640109300001"]},"isi":1,"quality_controlled":"1","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"}],"month":"04","publication_identifier":{"eissn":["1029-4945"],"issn":["0233-1934"]},"author":[{"full_name":"Ogbuisi, Ferdinard U.","last_name":"Ogbuisi","first_name":"Ferdinard U."},{"first_name":"Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini"},{"last_name":"Yao","first_name":"Jen Chih","full_name":"Yao, Jen Chih"}],"date_updated":"2023-10-10T09:48:41Z","date_created":"2021-05-02T22:01:29Z","year":"2021","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).","publication_status":"published","department":[{"_id":"VlKo"}],"publisher":"Taylor and Francis","ec_funded":1,"date_published":"2021-04-14T00:00:00Z","publication":"Optimization","citation":{"short":"F.U. Ogbuisi, Y. Shehu, J.C. Yao, Optimization (2021).","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.","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.","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","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.","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","ista":"Ogbuisi FU, Shehu Y, Yao JC. 2021. Convergence analysis of new inertial method for the split common null point problem. Optimization."},"article_type":"original","day":"14","article_processing_charge":"No","scopus_import":"1","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9365","title":"Convergence analysis of new inertial method for the split common null point problem","status":"public","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."}],"type":"journal_article"},{"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000559345400001"]},"isi":1,"quality_controlled":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"}],"doi":"10.1007/s11081-020-09544-5","language":[{"iso":"eng"}],"month":"02","publication_identifier":{"issn":["1389-4420"],"eissn":["1573-2924"]},"year":"2021","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.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"VlKo"}],"author":[{"orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini","full_name":"Shehu, Yekini"},{"full_name":"Dong, Qiao-Li","last_name":"Dong","first_name":"Qiao-Li"},{"full_name":"Liu, Lu-Lu","last_name":"Liu","first_name":"Lu-Lu"},{"last_name":"Yao","first_name":"Jen-Chih","full_name":"Yao, Jen-Chih"}],"date_updated":"2024-03-07T14:39:29Z","date_created":"2020-08-03T14:29:57Z","volume":22,"file_date_updated":"2020-08-03T15:24:39Z","ec_funded":1,"publication":"Optimization and Engineering","citation":{"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.","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.","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","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","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.","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."},"article_type":"original","page":"2627-2653","date_published":"2021-02-25T00:00:00Z","scopus_import":"1","day":"25","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","_id":"8196","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"title":"New strong convergence method for the sum of two maximal monotone operators","status":"public","intvolume":" 22","file":[{"date_created":"2020-08-03T15:24:39Z","date_updated":"2020-08-03T15:24:39Z","success":1,"relation":"main_file","file_id":"8197","content_type":"application/pdf","file_size":2137860,"creator":"dernst","file_name":"2020_OptimizationEngineering_Shehu.pdf","access_level":"open_access"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"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.","lang":"eng"}]},{"type":"journal_article","abstract":[{"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.","lang":"eng"}],"intvolume":" 15","title":"New inertial relaxed method for solving split feasibilities","status":"public","ddc":["510"],"_id":"7925","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"success":1,"checksum":"63c5f31cd04626152a19f97a2476281b","date_created":"2024-03-07T14:58:51Z","date_updated":"2024-03-07T14:58:51Z","file_id":"15089","relation":"main_file","creator":"kschuh","content_type":"application/pdf","file_size":2148882,"access_level":"open_access","file_name":"2021_OptimizationLetters_Shehu.pdf"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","page":"2109-2126","article_type":"original","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","ista":"Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities. Optimization Letters. 15, 2109–2126.","ieee":"Y. Shehu and A. Gibali, “New inertial relaxed method for solving split feasibilities,” Optimization Letters, vol. 15. Springer Nature, pp. 2109–2126, 2021.","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","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.","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."},"publication":"Optimization Letters","date_published":"2021-09-01T00:00:00Z","ec_funded":1,"file_date_updated":"2024-03-07T14:58:51Z","publisher":"Springer Nature","department":[{"_id":"VlKo"}],"publication_status":"published","year":"2021","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).","volume":15,"date_updated":"2024-03-07T15:00:43Z","date_created":"2020-06-04T11:28:33Z","author":[{"last_name":"Shehu","first_name":"Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","full_name":"Shehu, Yekini"},{"last_name":"Gibali","first_name":"Aviv","full_name":"Gibali, Aviv"}],"publication_identifier":{"eissn":["1862-4480"],"issn":["1862-4472"]},"month":"09","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000537342300001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s11590-020-01603-1"},{"publication_status":"published","department":[{"_id":"VlKo"}],"publisher":"Springer Nature","year":"2020","acknowledgement":"The research of this author is supported by the ERC grant at the IST.","date_updated":"2023-08-17T13:51:18Z","date_created":"2019-06-27T20:09:33Z","volume":84,"author":[{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini"},{"last_name":"Li","first_name":"Xiao-Huan","full_name":"Li, Xiao-Huan"},{"full_name":"Dong, Qiao-Li","last_name":"Dong","first_name":"Qiao-Li"}],"file_date_updated":"2020-07-14T12:47:34Z","ec_funded":1,"quality_controlled":"1","isi":1,"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"oa":1,"external_id":{"isi":["000528979000015"]},"language":[{"iso":"eng"}],"doi":"10.1007/s11075-019-00758-y","month":"05","publication_identifier":{"issn":["1017-1398"],"eissn":["1572-9265"]},"title":"An efficient projection-type method for monotone variational inequalities in Hilbert spaces","status":"public","ddc":["000"],"intvolume":" 84","_id":"6593","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"checksum":"bb1a1eb3ebb2df380863d0db594673ba","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-10-01T13:14:10Z","file_id":"6927","relation":"main_file","creator":"kschuh","content_type":"application/pdf","file_size":359654,"access_level":"open_access","file_name":"ExtragradientMethodPaper.pdf"}],"oa_version":"Submitted Version","type":"journal_article","abstract":[{"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.","lang":"eng"}],"article_type":"original","page":"365-388","publication":"Numerical Algorithms","citation":{"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.","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.","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.","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.","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","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"},"date_published":"2020-05-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","has_accepted_license":"1"},{"oa":1,"external_id":{"isi":["000564648400018"]},"project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","doi":"10.1016/j.apnum.2020.06.009","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0168-9274"]},"month":"11","year":"2020","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).","department":[{"_id":"VlKo"}],"publisher":"Elsevier","publication_status":"published","author":[{"orcid":"0000-0001-9224-7139","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","first_name":"Yekini","full_name":"Shehu, Yekini"},{"last_name":"Iyiola","first_name":"Olaniyi S.","full_name":"Iyiola, Olaniyi S."}],"volume":157,"date_created":"2020-07-02T09:02:33Z","date_updated":"2023-08-22T07:50:43Z","ec_funded":1,"file_date_updated":"2020-07-14T12:48:09Z","citation":{"short":"Y. Shehu, O.S. Iyiola, Applied Numerical Mathematics 157 (2020) 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.","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.","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","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.","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","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."},"publication":"Applied Numerical Mathematics","page":"315-337","article_type":"original","date_published":"2020-11-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8077","intvolume":" 157","title":"Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence","ddc":["510"],"status":"public","oa_version":"Submitted Version","file":[{"file_size":2874203,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2020_AppliedNumericalMath_Shehu.pdf","checksum":"87d81324a62c82baa925c009dfcb0200","date_updated":"2020-07-14T12:48:09Z","date_created":"2020-07-02T09:08:59Z","relation":"main_file","file_id":"8078"}],"type":"journal_article","abstract":[{"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.","lang":"eng"}]},{"type":"journal_article","abstract":[{"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.","lang":"eng"}],"title":"Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces","ddc":["518","510","515"],"status":"public","intvolume":" 184","_id":"7161","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"content_type":"application/pdf","file_size":332641,"creator":"dernst","access_level":"open_access","file_name":"2020_JourOptimizationTheoryApplic_Shehu.pdf","checksum":"9f6dc6c6bf2b48cb3a2091a9ed5feaf2","date_created":"2020-10-12T10:40:27Z","date_updated":"2021-03-16T23:30:04Z","relation":"main_file","file_id":"8647","embargo":"2021-03-15"}],"oa_version":"Submitted Version","scopus_import":"1","day":"01","article_processing_charge":"No","has_accepted_license":"1","article_type":"original","page":"877–894","publication":"Journal of Optimization Theory and Applications","citation":{"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.","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.","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","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.","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","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."},"date_published":"2020-03-01T00:00:00Z","file_date_updated":"2021-03-16T23:30:04Z","ec_funded":1,"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"VlKo"}],"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).","year":"2020","date_created":"2019-12-09T21:33:44Z","date_updated":"2023-09-06T11:27:15Z","volume":184,"author":[{"first_name":"Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini"},{"full_name":"Gibali, Aviv","first_name":"Aviv","last_name":"Gibali"},{"full_name":"Sagratella, Simone","first_name":"Simone","last_name":"Sagratella"}],"month":"03","publication_identifier":{"eissn":["1573-2878"],"issn":["0022-3239"]},"quality_controlled":"1","isi":1,"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"oa":1,"external_id":{"isi":["000511805200009"]},"language":[{"iso":"eng"}],"doi":"10.1007/s10957-019-01616-6"}]