[{"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"article_processing_charge":"No","external_id":{"arxiv":["2101.08057"],"isi":["000518364100001"]},"author":[{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu"},{"first_name":"Olaniyi S.","last_name":"Iyiola","full_name":"Iyiola, Olaniyi S."}],"title":"Weak convergence for variational inequalities with inertial-type method","citation":{"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.","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.","short":"Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216.","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.","ista":"Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"Taylor & Francis","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).","page":"192-216","date_created":"2020-03-09T07:06:52Z","doi":"10.1080/00036811.2020.1736287","date_published":"2022-01-01T00:00:00Z","year":"2022","has_accepted_license":"1","isi":1,"publication":"Applicable Analysis","day":"01","article_type":"original","type":"journal_article","status":"public","_id":"7577","department":[{"_id":"VlKo"}],"file_date_updated":"2021-03-16T23:30:06Z","date_updated":"2024-03-05T14:01:52Z","ddc":["510","515","518"],"scopus_import":"1","intvolume":" 101","month":"01","abstract":[{"text":"Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods.","lang":"eng"}],"oa_version":"Submitted Version","ec_funded":1,"volume":101,"issue":"1","publication_status":"published","publication_identifier":{"issn":["0003-6811"],"eissn":["1563-504X"]},"language":[{"iso":"eng"}],"file":[{"file_id":"8648","checksum":"869efe8cb09505dfa6012f67d20db63d","embargo":"2021-03-15","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2020-10-12T10:42:54Z","file_name":"2020_ApplicAnalysis_Shehu.pdf","creator":"dernst","date_updated":"2021-03-16T23:30:06Z","file_size":4282586}]},{"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1055-6788"],"eissn":["1029-4937"]},"publication_status":"published","ec_funded":1,"oa_version":"None","abstract":[{"text":"In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis.","lang":"eng"}],"month":"05","scopus_import":"1","date_updated":"2023-08-08T13:57:43Z","department":[{"_id":"VlKo"}],"_id":"9469","status":"public","article_type":"original","type":"journal_article","day":"12","publication":"Optimization Methods and Software","isi":1,"year":"2021","date_published":"2021-05-12T00:00:00Z","doi":"10.1080/10556788.2021.1924715","date_created":"2021-06-06T22:01:30Z","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).","quality_controlled":"1","publisher":"Taylor and Francis","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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","short":"O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software (2021).","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.","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.","ista":"Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software.","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."},"title":"Reflected three-operator splitting method for monotone inclusion problem","author":[{"first_name":"Olaniyi S.","last_name":"Iyiola","full_name":"Iyiola, Olaniyi S."},{"last_name":"Enyi","full_name":"Enyi, Cyril D.","first_name":"Cyril D."},{"first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139"}],"article_processing_charge":"No","external_id":{"isi":["000650507600001"]},"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}]},{"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"title":"New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000625002100001"]},"author":[{"first_name":"Chinedu","full_name":"Izuchukwu, Chinedu","last_name":"Izuchukwu"},{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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.","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","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"},"oa":1,"quality_controlled":"1","publisher":"Springer Nature","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_published":"2021-06-01T00:00:00Z","doi":"10.1007/s11067-021-09517-w","page":"291-323","publication":"Networks and Spatial Economics","day":"01","year":"2021","has_accepted_license":"1","isi":1,"keyword":["Computer Networks and Communications","Software","Artificial Intelligence"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"9234","department":[{"_id":"VlKo"}],"file_date_updated":"2021-08-11T12:44:16Z","ddc":["510"],"date_updated":"2023-09-05T15:32:32Z","intvolume":" 21","month":"06","scopus_import":"1","oa_version":"Published Version","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."}],"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"volume":21,"issue":"2","language":[{"iso":"eng"}],"file":[{"file_size":834964,"date_updated":"2021-08-11T12:44:16Z","creator":"kschuh","file_name":"2021_NetworksSpatialEconomics_Shehu.pdf","date_created":"2021-08-11T12:44:16Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"22b4253a2e5da843622a2df713784b4c","file_id":"9884"}],"publication_status":"published","publication_identifier":{"eissn":["1572-9427"],"issn":["1566-113X"]}},{"type":"journal_article","article_type":"original","status":"public","_id":"8817","department":[{"_id":"VlKo"}],"date_updated":"2023-10-10T09:30:23Z","scopus_import":"1","month":"04","intvolume":" 93","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."}],"oa_version":"None","issue":"2","volume":93,"ec_funded":1,"publication_identifier":{"eissn":["1432-5217"],"issn":["1432-2994"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"author":[{"first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","last_name":"Shehu"},{"full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola","first_name":"Olaniyi S."},{"first_name":"Duong Viet","full_name":"Thong, Duong Viet","last_name":"Thong"},{"last_name":"Van","full_name":"Van, Nguyen Thi Cam","first_name":"Nguyen Thi Cam"}],"external_id":{"isi":["000590497300001"]},"article_processing_charge":"No","title":"An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems","citation":{"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.","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.","short":"Y. Shehu, O.S. Iyiola, D.V. Thong, N.T.C. Van, Mathematical Methods of Operations Research 93 (2021) 213–242.","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","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Springer Nature","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).","page":"213-242","doi":"10.1007/s00186-020-00730-w","date_published":"2021-04-01T00:00:00Z","date_created":"2020-11-29T23:01:18Z","isi":1,"year":"2021","day":"01","publication":"Mathematical Methods of Operations Research"},{"department":[{"_id":"VlKo"}],"date_updated":"2023-10-10T09:47:33Z","type":"journal_article","article_type":"original","status":"public","_id":"9315","issue":"2","volume":76,"publication_status":"published","publication_identifier":{"eissn":["1420-9012"],"issn":["1422-6383"]},"language":[{"iso":"eng"}],"scopus_import":"1","intvolume":" 76","month":"03","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."}],"oa_version":"None","article_processing_charge":"No","external_id":{"isi":["000632917700001"]},"author":[{"full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola","first_name":"Olaniyi S."},{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"}],"title":"New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications","citation":{"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).","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.","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","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","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"75","date_created":"2021-04-11T22:01:14Z","doi":"10.1007/s00025-021-01381-x","date_published":"2021-03-25T00:00:00Z","year":"2021","isi":1,"publication":"Results in Mathematics","day":"25","publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria."},{"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).","quality_controlled":"1","publisher":"Taylor and Francis","publication":"Optimization","day":"14","year":"2021","isi":1,"date_created":"2021-05-02T22:01:29Z","date_published":"2021-04-14T00:00:00Z","doi":"10.1080/02331934.2021.1914035","project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Ogbuisi FU, Shehu Y, Yao JC. 2021. Convergence analysis of new inertial method for the split common null point problem. Optimization.","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.","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","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.","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."},"title":"Convergence analysis of new inertial method for the split common null point problem","article_processing_charge":"No","external_id":{"isi":["000640109300001"]},"author":[{"full_name":"Ogbuisi, Ferdinard U.","last_name":"Ogbuisi","first_name":"Ferdinard U."},{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","last_name":"Shehu"},{"last_name":"Yao","full_name":"Yao, Jen Chih","first_name":"Jen Chih"}],"oa_version":"None","abstract":[{"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.","lang":"eng"}],"month":"04","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0233-1934"],"eissn":["1029-4945"]},"ec_funded":1,"_id":"9365","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-10-10T09:48:41Z","department":[{"_id":"VlKo"}]},{"scopus_import":"1","intvolume":" 22","month":"02","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."}],"oa_version":"Published Version","ec_funded":1,"volume":22,"publication_status":"published","publication_identifier":{"issn":["1389-4420"],"eissn":["1573-2924"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2020-08-03T15:24:39Z","file_name":"2020_OptimizationEngineering_Shehu.pdf","date_updated":"2020-08-03T15:24:39Z","file_size":2137860,"creator":"dernst","file_id":"8197","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"8196","file_date_updated":"2020-08-03T15:24:39Z","department":[{"_id":"VlKo"}],"date_updated":"2024-03-07T14:39:29Z","ddc":["510"],"oa":1,"publisher":"Springer Nature","quality_controlled":"1","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.","page":"2627-2653","date_created":"2020-08-03T14:29:57Z","date_published":"2021-02-25T00:00:00Z","doi":"10.1007/s11081-020-09544-5","year":"2021","has_accepted_license":"1","isi":1,"publication":"Optimization and Engineering","day":"25","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000559345400001"]},"author":[{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Dong, Qiao-Li","last_name":"Dong","first_name":"Qiao-Li"},{"last_name":"Liu","full_name":"Liu, Lu-Lu","first_name":"Lu-Lu"},{"first_name":"Jen-Chih","last_name":"Yao","full_name":"Yao, Jen-Chih"}],"title":"New strong convergence method for the sum of two maximal monotone operators","citation":{"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","short":"Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering 22 (2021) 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.","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.","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.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"ddc":["510"],"date_updated":"2024-03-07T15:00:43Z","department":[{"_id":"VlKo"}],"file_date_updated":"2024-03-07T14:58:51Z","_id":"7925","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"63c5f31cd04626152a19f97a2476281b","file_id":"15089","success":1,"date_updated":"2024-03-07T14:58:51Z","file_size":2148882,"creator":"kschuh","date_created":"2024-03-07T14:58:51Z","file_name":"2021_OptimizationLetters_Shehu.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1862-4480"],"issn":["1862-4472"]},"publication_status":"published","volume":15,"ec_funded":1,"oa_version":"Published Version","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."}],"month":"09","intvolume":" 15","scopus_import":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"short":"Y. Shehu, A. Gibali, Optimization Letters 15 (2021) 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","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","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.","ista":"Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities. Optimization Letters. 15, 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."},"title":"New inertial relaxed method for solving split feasibilities","author":[{"first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","last_name":"Shehu","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini"},{"first_name":"Aviv","last_name":"Gibali","full_name":"Gibali, Aviv"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000537342300001"]},"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"day":"01","publication":"Optimization Letters","has_accepted_license":"1","isi":1,"year":"2021","doi":"10.1007/s11590-020-01603-1","date_published":"2021-09-01T00:00:00Z","date_created":"2020-06-04T11:28:33Z","page":"2109-2126","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).","publisher":"Springer Nature","quality_controlled":"1","oa":1},{"citation":{"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.","short":"Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.","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","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000528979000015"]},"article_processing_charge":"No","author":[{"orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"},{"first_name":"Xiao-Huan","full_name":"Li, Xiao-Huan","last_name":"Li"},{"first_name":"Qiao-Li","full_name":"Dong, Qiao-Li","last_name":"Dong"}],"title":"An efficient projection-type method for monotone variational inequalities in Hilbert spaces","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"year":"2020","has_accepted_license":"1","isi":1,"publication":"Numerical Algorithms","day":"01","page":"365-388","date_created":"2019-06-27T20:09:33Z","doi":"10.1007/s11075-019-00758-y","date_published":"2020-05-01T00:00:00Z","acknowledgement":"The research of this author is supported by the ERC grant at the IST.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","date_updated":"2023-08-17T13:51:18Z","ddc":["000"],"department":[{"_id":"VlKo"}],"file_date_updated":"2020-07-14T12:47:34Z","_id":"6593","article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["1572-9265"],"issn":["1017-1398"]},"language":[{"iso":"eng"}],"file":[{"file_name":"ExtragradientMethodPaper.pdf","date_created":"2019-10-01T13:14:10Z","creator":"kschuh","file_size":359654,"date_updated":"2020-07-14T12:47:34Z","file_id":"6927","checksum":"bb1a1eb3ebb2df380863d0db594673ba","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"ec_funded":1,"volume":84,"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."}],"oa_version":"Submitted Version","scopus_import":"1","intvolume":" 84","month":"05"},{"language":[{"iso":"eng"}],"file":[{"file_size":2874203,"date_updated":"2020-07-14T12:48:09Z","creator":"dernst","file_name":"2020_AppliedNumericalMath_Shehu.pdf","date_created":"2020-07-02T09:08:59Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"8078","checksum":"87d81324a62c82baa925c009dfcb0200"}],"publication_status":"published","publication_identifier":{"issn":["0168-9274"]},"ec_funded":1,"volume":157,"oa_version":"Submitted Version","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"}],"intvolume":" 157","month":"11","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-22T07:50:43Z","file_date_updated":"2020-07-14T12:48:09Z","department":[{"_id":"VlKo"}],"_id":"8077","status":"public","type":"journal_article","article_type":"original","publication":"Applied Numerical Mathematics","day":"01","year":"2020","has_accepted_license":"1","isi":1,"date_created":"2020-07-02T09:02:33Z","doi":"10.1016/j.apnum.2020.06.009","date_published":"2020-11-01T00:00:00Z","page":"315-337","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).","oa":1,"publisher":"Elsevier","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","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","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.","short":"Y. Shehu, O.S. Iyiola, Applied Numerical Mathematics 157 (2020) 315–337."},"title":"Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence","article_processing_charge":"No","external_id":{"isi":["000564648400018"]},"author":[{"last_name":"Shehu","full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Olaniyi S.","full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola"}],"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"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).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","publication":"Journal of Optimization Theory and Applications","day":"01","year":"2020","has_accepted_license":"1","isi":1,"date_created":"2019-12-09T21:33:44Z","date_published":"2020-03-01T00:00:00Z","doi":"10.1007/s10957-019-01616-6","page":"877–894","project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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.","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.","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."},"title":"Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces","article_processing_charge":"No","external_id":{"isi":["000511805200009"]},"author":[{"last_name":"Shehu","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gibali, Aviv","last_name":"Gibali","first_name":"Aviv"},{"full_name":"Sagratella, Simone","last_name":"Sagratella","first_name":"Simone"}],"oa_version":"Submitted Version","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"}],"intvolume":" 184","month":"03","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"date_updated":"2021-03-16T23:30:04Z","file_size":332641,"creator":"dernst","date_created":"2020-10-12T10:40:27Z","file_name":"2020_JourOptimizationTheoryApplic_Shehu.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"9f6dc6c6bf2b48cb3a2091a9ed5feaf2","file_id":"8647","embargo":"2021-03-15"}],"publication_status":"published","publication_identifier":{"issn":["0022-3239"],"eissn":["1573-2878"]},"ec_funded":1,"volume":184,"_id":"7161","status":"public","type":"journal_article","article_type":"original","ddc":["518","510","515"],"date_updated":"2023-09-06T11:27:15Z","file_date_updated":"2021-03-16T23:30:04Z","department":[{"_id":"VlKo"}]},{"citation":{"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.","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.","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","short":"Y. Shehu, Results in Mathematics 74 (2019).","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["2101.09068"],"isi":["000473237500002"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Shehu","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","first_name":"Yekini"}],"title":"Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces","article_number":"138","project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"year":"2019","isi":1,"has_accepted_license":"1","publication":"Results in Mathematics","day":"01","date_created":"2019-06-29T10:11:30Z","doi":"10.1007/s00025-019-1061-4","date_published":"2019-12-01T00:00:00Z","oa":1,"publisher":"Springer","quality_controlled":"1","date_updated":"2023-08-28T12:26:22Z","ddc":["000"],"department":[{"_id":"VlKo"}],"file_date_updated":"2020-07-14T12:47:34Z","_id":"6596","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["1420-9012"],"issn":["1422-6383"]},"language":[{"iso":"eng"}],"file":[{"creator":"kschuh","date_updated":"2020-07-14T12:47:34Z","file_size":466942,"date_created":"2019-07-03T15:20:40Z","file_name":"Springer_2019_Shehu.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"c6d18cb1e16fc0c36a0e0f30b4ebbc2d","file_id":"6605"}],"ec_funded":1,"issue":"4","volume":74,"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 74","month":"12"},{"doi":"10.1007/s40314-019-0955-9","date_published":"2019-12-01T00:00:00Z","date_created":"2019-11-12T12:41:44Z","day":"01","publication":"Computational and Applied Mathematics","has_accepted_license":"1","isi":1,"year":"2019","publisher":"Springer Nature","quality_controlled":"1","oa":1,"title":"Convergence analysis of projection method for variational inequalities","author":[{"full_name":"Shehu, Yekini","orcid":"0000-0001-9224-7139","last_name":"Shehu","first_name":"Yekini","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Iyiola, Olaniyi S.","last_name":"Iyiola","first_name":"Olaniyi S."},{"last_name":"Li","full_name":"Li, Xiao-Huan","first_name":"Xiao-Huan"},{"full_name":"Dong, Qiao-Li","last_name":"Dong","first_name":"Qiao-Li"}],"article_processing_charge":"No","external_id":{"isi":["000488973100005"],"arxiv":["2101.09081"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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).","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.","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.","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."},"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"161","issue":"4","volume":38,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1807-0302"],"issn":["2238-3603"]},"publication_status":"published","month":"12","intvolume":" 38","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s40314-019-0955-9"}],"oa_version":"Published Version","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."}],"department":[{"_id":"VlKo"}],"ddc":["510","515","518"],"date_updated":"2023-08-30T07:20:32Z","status":"public","article_type":"original","type":"journal_article","_id":"7000"}]