--- _id: '7577' abstract: - lang: eng text: Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods. acknowledgement: The project of the first author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola citation: ama: Shehu Y, Iyiola OS. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 2022;101(1):192-216. doi:10.1080/00036811.2020.1736287 apa: Shehu, Y., & Iyiola, O. S. (2022). Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. Taylor & Francis. https://doi.org/10.1080/00036811.2020.1736287 chicago: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis. Taylor & Francis, 2022. https://doi.org/10.1080/00036811.2020.1736287. ieee: Y. Shehu and O. S. Iyiola, “Weak convergence for variational inequalities with inertial-type method,” Applicable Analysis, vol. 101, no. 1. Taylor & Francis, pp. 192–216, 2022. ista: Shehu Y, Iyiola OS. 2022. Weak convergence for variational inequalities with inertial-type method. Applicable Analysis. 101(1), 192–216. mla: Shehu, Yekini, and Olaniyi S. Iyiola. “Weak Convergence for Variational Inequalities with Inertial-Type Method.” Applicable Analysis, vol. 101, no. 1, Taylor & Francis, 2022, pp. 192–216, doi:10.1080/00036811.2020.1736287. short: Y. Shehu, O.S. Iyiola, Applicable Analysis 101 (2022) 192–216. date_created: 2020-03-09T07:06:52Z date_published: 2022-01-01T00:00:00Z date_updated: 2024-03-05T14:01:52Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1080/00036811.2020.1736287 ec_funded: 1 external_id: arxiv: - '2101.08057' isi: - '000518364100001' file: - access_level: open_access checksum: 869efe8cb09505dfa6012f67d20db63d content_type: application/pdf creator: dernst date_created: 2020-10-12T10:42:54Z date_updated: 2021-03-16T23:30:06Z embargo: 2021-03-15 file_id: '8648' file_name: 2020_ApplicAnalysis_Shehu.pdf file_size: 4282586 relation: main_file file_date_updated: 2021-03-16T23:30:06Z has_accepted_license: '1' intvolume: ' 101' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 192-216 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Applicable Analysis publication_identifier: eissn: - 1563-504X issn: - 0003-6811 publication_status: published publisher: Taylor & Francis quality_controlled: '1' scopus_import: '1' status: public title: Weak convergence for variational inequalities with inertial-type method type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 101 year: '2022' ... --- _id: '9469' abstract: - lang: eng text: In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis. acknowledgement: The authors are grateful to the anonymous referees and the handling Editor for their insightful comments which have improved the earlier version of the manuscript greatly. The second author is grateful to the University of Hafr Al Batin. The last author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Cyril D. full_name: Enyi, Cyril D. last_name: Enyi - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 2021. doi:10.1080/10556788.2021.1924715 apa: Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2021). Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. Taylor and Francis. https://doi.org/10.1080/10556788.2021.1924715 chicago: Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software. Taylor and Francis, 2021. https://doi.org/10.1080/10556788.2021.1924715. ieee: O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” Optimization Methods and Software. Taylor and Francis, 2021. ista: Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. mla: Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software, Taylor and Francis, 2021, doi:10.1080/10556788.2021.1924715. short: O.S. Iyiola, C.D. Enyi, Y. Shehu, Optimization Methods and Software (2021). date_created: 2021-06-06T22:01:30Z date_published: 2021-05-12T00:00:00Z date_updated: 2023-08-08T13:57:43Z day: '12' department: - _id: VlKo doi: 10.1080/10556788.2021.1924715 ec_funded: 1 external_id: isi: - '000650507600001' isi: 1 language: - iso: eng month: '05' oa_version: None project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Optimization Methods and Software publication_identifier: eissn: - 1029-4937 issn: - 1055-6788 publication_status: published publisher: Taylor and Francis quality_controlled: '1' scopus_import: '1' status: public title: Reflected three-operator splitting method for monotone inclusion problem type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '9234' abstract: - lang: eng text: In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps. acknowledgement: 'The authors sincerely thank the Editor-in-Chief and anonymous referees for their careful reading, constructive comments and fruitful suggestions that help improve the manuscript. The research of the first author is supported by the National Research Foundation (NRF) South Africa (S& F-DSI/NRF Free Standing Postdoctoral Fellowship; Grant Number: 120784). The first author also acknowledges the financial support from DSI/NRF, South Africa Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Postdoctoral Fellowship. The second author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). Open Access funding provided by Institute of Science and Technology (IST Austria).' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Chinedu full_name: Izuchukwu, Chinedu last_name: Izuchukwu - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Izuchukwu C, Shehu Y. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. 2021;21(2):291-323. doi:10.1007/s11067-021-09517-w apa: Izuchukwu, C., & Shehu, Y. (2021). New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. Springer Nature. https://doi.org/10.1007/s11067-021-09517-w chicago: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks and Spatial Economics. Springer Nature, 2021. https://doi.org/10.1007/s11067-021-09517-w. ieee: C. Izuchukwu and Y. Shehu, “New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity,” Networks and Spatial Economics, vol. 21, no. 2. Springer Nature, pp. 291–323, 2021. ista: Izuchukwu C, Shehu Y. 2021. New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity. Networks and Spatial Economics. 21(2), 291–323. mla: Izuchukwu, Chinedu, and Yekini Shehu. “New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems beyond Monotonicity.” Networks and Spatial Economics, vol. 21, no. 2, Springer Nature, 2021, pp. 291–323, doi:10.1007/s11067-021-09517-w. short: C. Izuchukwu, Y. Shehu, Networks and Spatial Economics 21 (2021) 291–323. date_created: 2021-03-10T12:18:47Z date_published: 2021-06-01T00:00:00Z date_updated: 2023-09-05T15:32:32Z day: '01' ddc: - '510' department: - _id: VlKo doi: 10.1007/s11067-021-09517-w ec_funded: 1 external_id: isi: - '000625002100001' file: - access_level: open_access checksum: 22b4253a2e5da843622a2df713784b4c content_type: application/pdf creator: kschuh date_created: 2021-08-11T12:44:16Z date_updated: 2021-08-11T12:44:16Z file_id: '9884' file_name: 2021_NetworksSpatialEconomics_Shehu.pdf file_size: 834964 relation: main_file success: 1 file_date_updated: 2021-08-11T12:44:16Z has_accepted_license: '1' intvolume: ' 21' isi: 1 issue: '2' keyword: - Computer Networks and Communications - Software - Artificial Intelligence language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 291-323 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Networks and Spatial Economics publication_identifier: eissn: - 1572-9427 issn: - 1566-113X publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 21 year: '2021' ... --- _id: '8817' abstract: - lang: eng text: The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model. acknowledgement: The authors are grateful to the two referees and the Associate Editor for their comments and suggestions which have improved the earlier version of the paper greatly. The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Duong Viet full_name: Thong, Duong Viet last_name: Thong - first_name: Nguyen Thi Cam full_name: Van, Nguyen Thi Cam last_name: Van citation: ama: Shehu Y, Iyiola OS, Thong DV, Van NTC. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 2021;93(2):213-242. doi:10.1007/s00186-020-00730-w apa: Shehu, Y., Iyiola, O. S., Thong, D. V., & Van, N. T. C. (2021). An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. Springer Nature. https://doi.org/10.1007/s00186-020-00730-w chicago: Shehu, Yekini, Olaniyi S. Iyiola, Duong Viet Thong, and Nguyen Thi Cam Van. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research. Springer Nature, 2021. https://doi.org/10.1007/s00186-020-00730-w. ieee: Y. Shehu, O. S. Iyiola, D. V. Thong, and N. T. C. Van, “An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems,” Mathematical Methods of Operations Research, vol. 93, no. 2. Springer Nature, pp. 213–242, 2021. ista: Shehu Y, Iyiola OS, Thong DV, Van NTC. 2021. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 93(2), 213–242. mla: Shehu, Yekini, et al. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research, vol. 93, no. 2, Springer Nature, 2021, pp. 213–42, doi:10.1007/s00186-020-00730-w. short: Y. Shehu, O.S. Iyiola, D.V. Thong, N.T.C. Van, Mathematical Methods of Operations Research 93 (2021) 213–242. date_created: 2020-11-29T23:01:18Z date_published: 2021-04-01T00:00:00Z date_updated: 2023-10-10T09:30:23Z day: '01' department: - _id: VlKo doi: 10.1007/s00186-020-00730-w ec_funded: 1 external_id: isi: - '000590497300001' intvolume: ' 93' isi: 1 issue: '2' language: - iso: eng month: '04' oa_version: None page: 213-242 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Mathematical Methods of Operations Research publication_identifier: eissn: - 1432-5217 issn: - 1432-2994 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 93 year: '2021' ... --- _id: '9315' abstract: - lang: eng text: We consider inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. To do these, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the inertial Krasnoselskii–Mann iteration for fixed point of nonexpansive operators in infinite dimensional real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature. We then show that Fermat–Weber location problem and primal–dual three-operator splitting are special cases of fixed point problem of nonexpansive mapping and consequently obtain the convergence analysis of inertial iteration methods for Fermat–Weber location problem and primal–dual three-operator splitting in real Hilbert spaces. Some numerical implementations are drawn from primal–dual three-operator splitting to support the theoretical analysis. acknowledgement: The research of this author is supported by the Postdoctoral Fellowship from Institute of Science and Technology (IST), Austria. article_number: '75' article_processing_charge: No article_type: original author: - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Iyiola OS, Shehu Y. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 2021;76(2). doi:10.1007/s00025-021-01381-x apa: Iyiola, O. S., & Shehu, Y. (2021). New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. Springer Nature. https://doi.org/10.1007/s00025-021-01381-x chicago: Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results in Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s00025-021-01381-x. ieee: O. S. Iyiola and Y. Shehu, “New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications,” Results in Mathematics, vol. 76, no. 2. Springer Nature, 2021. ista: Iyiola OS, Shehu Y. 2021. New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications. Results in Mathematics. 76(2), 75. mla: Iyiola, Olaniyi S., and Yekini Shehu. “New Convergence Results for Inertial Krasnoselskii–Mann Iterations in Hilbert Spaces with Applications.” Results in Mathematics, vol. 76, no. 2, 75, Springer Nature, 2021, doi:10.1007/s00025-021-01381-x. short: O.S. Iyiola, Y. Shehu, Results in Mathematics 76 (2021). date_created: 2021-04-11T22:01:14Z date_published: 2021-03-25T00:00:00Z date_updated: 2023-10-10T09:47:33Z day: '25' department: - _id: VlKo doi: 10.1007/s00025-021-01381-x external_id: isi: - '000632917700001' intvolume: ' 76' isi: 1 issue: '2' language: - iso: eng month: '03' oa_version: None publication: Results in Mathematics publication_identifier: eissn: - 1420-9012 issn: - 1422-6383 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: New convergence results for inertial Krasnoselskii–Mann iterations in Hilbert spaces with applications type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 76 year: '2021' ... --- _id: '9365' abstract: - lang: eng text: In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method. acknowledgement: The second author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Ferdinard U. full_name: Ogbuisi, Ferdinard U. last_name: Ogbuisi - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Jen Chih full_name: Yao, Jen Chih last_name: Yao citation: ama: Ogbuisi FU, Shehu Y, Yao JC. Convergence analysis of new inertial method for the split common null point problem. Optimization. 2021. doi:10.1080/02331934.2021.1914035 apa: Ogbuisi, F. U., Shehu, Y., & Yao, J. C. (2021). Convergence analysis of new inertial method for the split common null point problem. Optimization. Taylor and Francis. https://doi.org/10.1080/02331934.2021.1914035 chicago: Ogbuisi, Ferdinard U., Yekini Shehu, and Jen Chih Yao. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization. Taylor and Francis, 2021. https://doi.org/10.1080/02331934.2021.1914035. ieee: F. U. Ogbuisi, Y. Shehu, and J. C. Yao, “Convergence analysis of new inertial method for the split common null point problem,” Optimization. Taylor and Francis, 2021. ista: Ogbuisi FU, Shehu Y, Yao JC. 2021. Convergence analysis of new inertial method for the split common null point problem. Optimization. mla: Ogbuisi, Ferdinard U., et al. “Convergence Analysis of New Inertial Method for the Split Common Null Point Problem.” Optimization, Taylor and Francis, 2021, doi:10.1080/02331934.2021.1914035. short: F.U. Ogbuisi, Y. Shehu, J.C. Yao, Optimization (2021). date_created: 2021-05-02T22:01:29Z date_published: 2021-04-14T00:00:00Z date_updated: 2023-10-10T09:48:41Z day: '14' department: - _id: VlKo doi: 10.1080/02331934.2021.1914035 ec_funded: 1 external_id: isi: - '000640109300001' isi: 1 language: - iso: eng month: '04' oa_version: None project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Optimization publication_identifier: eissn: - 1029-4945 issn: - 0233-1934 publication_status: published publisher: Taylor and Francis quality_controlled: '1' scopus_import: '1' status: public title: Convergence analysis of new inertial method for the split common null point problem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '8196' abstract: - lang: eng text: This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7—2007–2013) (Grant Agreement No. 616160). The authors are grateful to the anonymous referees and the handling Editor for their comments and suggestions which have improved the earlier version of the manuscript greatly. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Qiao-Li full_name: Dong, Qiao-Li last_name: Dong - first_name: Lu-Lu full_name: Liu, Lu-Lu last_name: Liu - first_name: Jen-Chih full_name: Yao, Jen-Chih last_name: Yao citation: ama: Shehu Y, Dong Q-L, Liu L-L, Yao J-C. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 2021;22:2627-2653. doi:10.1007/s11081-020-09544-5 apa: Shehu, Y., Dong, Q.-L., Liu, L.-L., & Yao, J.-C. (2021). New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. Springer Nature. https://doi.org/10.1007/s11081-020-09544-5 chicago: Shehu, Yekini, Qiao-Li Dong, Lu-Lu Liu, and Jen-Chih Yao. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering. Springer Nature, 2021. https://doi.org/10.1007/s11081-020-09544-5. ieee: Y. Shehu, Q.-L. Dong, L.-L. Liu, and J.-C. Yao, “New strong convergence method for the sum of two maximal monotone operators,” Optimization and Engineering, vol. 22. Springer Nature, pp. 2627–2653, 2021. ista: Shehu Y, Dong Q-L, Liu L-L, Yao J-C. 2021. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 22, 2627–2653. mla: Shehu, Yekini, et al. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering, vol. 22, Springer Nature, 2021, pp. 2627–53, doi:10.1007/s11081-020-09544-5. short: Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering 22 (2021) 2627–2653. date_created: 2020-08-03T14:29:57Z date_published: 2021-02-25T00:00:00Z date_updated: 2024-03-07T14:39:29Z day: '25' ddc: - '510' department: - _id: VlKo doi: 10.1007/s11081-020-09544-5 ec_funded: 1 external_id: isi: - '000559345400001' file: - access_level: open_access content_type: application/pdf creator: dernst date_created: 2020-08-03T15:24:39Z date_updated: 2020-08-03T15:24:39Z file_id: '8197' file_name: 2020_OptimizationEngineering_Shehu.pdf file_size: 2137860 relation: main_file success: 1 file_date_updated: 2020-08-03T15:24:39Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 2627-2653 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Optimization and Engineering publication_identifier: eissn: - 1573-2924 issn: - 1389-4420 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: New strong convergence method for the sum of two maximal monotone operators tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 22 year: '2021' ... --- _id: '7925' abstract: - lang: eng text: In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). The authors are grateful to the referees for their insightful comments which have improved the earlier version of the manuscript greatly. The first author has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Aviv full_name: Gibali, Aviv last_name: Gibali citation: ama: Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities. Optimization Letters. 2021;15:2109-2126. doi:10.1007/s11590-020-01603-1 apa: Shehu, Y., & Gibali, A. (2021). New inertial relaxed method for solving split feasibilities. Optimization Letters. Springer Nature. https://doi.org/10.1007/s11590-020-01603-1 chicago: Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters. Springer Nature, 2021. https://doi.org/10.1007/s11590-020-01603-1. ieee: Y. Shehu and A. Gibali, “New inertial relaxed method for solving split feasibilities,” Optimization Letters, vol. 15. Springer Nature, pp. 2109–2126, 2021. ista: Shehu Y, Gibali A. 2021. New inertial relaxed method for solving split feasibilities. Optimization Letters. 15, 2109–2126. mla: Shehu, Yekini, and Aviv Gibali. “New Inertial Relaxed Method for Solving Split Feasibilities.” Optimization Letters, vol. 15, Springer Nature, 2021, pp. 2109–26, doi:10.1007/s11590-020-01603-1. short: Y. Shehu, A. Gibali, Optimization Letters 15 (2021) 2109–2126. date_created: 2020-06-04T11:28:33Z date_published: 2021-09-01T00:00:00Z date_updated: 2024-03-07T15:00:43Z day: '01' ddc: - '510' department: - _id: VlKo doi: 10.1007/s11590-020-01603-1 ec_funded: 1 external_id: isi: - '000537342300001' file: - access_level: open_access checksum: 63c5f31cd04626152a19f97a2476281b content_type: application/pdf creator: kschuh date_created: 2024-03-07T14:58:51Z date_updated: 2024-03-07T14:58:51Z file_id: '15089' file_name: 2021_OptimizationLetters_Shehu.pdf file_size: 2148882 relation: main_file success: 1 file_date_updated: 2024-03-07T14:58:51Z has_accepted_license: '1' intvolume: ' 15' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 2109-2126 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Optimization Letters publication_identifier: eissn: - 1862-4480 issn: - 1862-4472 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: New inertial relaxed method for solving split feasibilities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2021' ... --- _id: '6593' abstract: - lang: eng text: 'We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.' acknowledgement: The research of this author is supported by the ERC grant at the IST. article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Xiao-Huan full_name: Li, Xiao-Huan last_name: Li - first_name: Qiao-Li full_name: Dong, Qiao-Li last_name: Dong citation: ama: Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 2020;84:365-388. doi:10.1007/s11075-019-00758-y apa: Shehu, Y., Li, X.-H., & Dong, Q.-L. (2020). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. Springer Nature. https://doi.org/10.1007/s11075-019-00758-y chicago: Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms. Springer Nature, 2020. https://doi.org/10.1007/s11075-019-00758-y. ieee: Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for monotone variational inequalities in Hilbert spaces,” Numerical Algorithms, vol. 84. Springer Nature, pp. 365–388, 2020. ista: Shehu Y, Li X-H, Dong Q-L. 2020. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 84, 365–388. mla: Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms, vol. 84, Springer Nature, 2020, pp. 365–88, doi:10.1007/s11075-019-00758-y. short: Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388. date_created: 2019-06-27T20:09:33Z date_published: 2020-05-01T00:00:00Z date_updated: 2023-08-17T13:51:18Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.1007/s11075-019-00758-y ec_funded: 1 external_id: isi: - '000528979000015' file: - access_level: open_access checksum: bb1a1eb3ebb2df380863d0db594673ba content_type: application/pdf creator: kschuh date_created: 2019-10-01T13:14:10Z date_updated: 2020-07-14T12:47:34Z file_id: '6927' file_name: ExtragradientMethodPaper.pdf file_size: 359654 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 84' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Submitted Version page: 365-388 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Numerical Algorithms publication_identifier: eissn: - 1572-9265 issn: - 1017-1398 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: An efficient projection-type method for monotone variational inequalities in Hilbert spaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 84 year: '2020' ... --- _id: '8077' abstract: - lang: eng text: The projection methods with vanilla inertial extrapolation step for variational inequalities have been of interest to many authors recently due to the improved convergence speed contributed by the presence of inertial extrapolation step. However, it is discovered that these projection methods with inertial steps lose the Fejér monotonicity of the iterates with respect to the solution, which is being enjoyed by their corresponding non-inertial projection methods for variational inequalities. This lack of Fejér monotonicity makes projection methods with vanilla inertial extrapolation step for variational inequalities not to converge faster than their corresponding non-inertial projection methods at times. Also, it has recently been proved that the projection methods with vanilla inertial extrapolation step may provide convergence rates that are worse than the classical projected gradient methods for strongly convex functions. In this paper, we introduce projection methods with alternated inertial extrapolation step for solving variational inequalities. We show that the sequence of iterates generated by our methods converges weakly to a solution of the variational inequality under some appropriate conditions. The Fejér monotonicity of even subsequence is recovered in these methods and linear rate of convergence is obtained. The numerical implementations of our methods compared with some other inertial projection methods show that our method is more efficient and outperforms some of these inertial projection methods. acknowledgement: The authors are grateful to the two anonymous referees for their insightful comments and suggestions which have improved the earlier version of the manuscript greatly. The first author has received funding from the European Research Council (ERC) under the European Union Seventh Framework Programme (FP7 - 2007-2013) (Grant agreement No. 616160). article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola citation: ama: 'Shehu Y, Iyiola OS. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. 2020;157:315-337. doi:10.1016/j.apnum.2020.06.009' apa: 'Shehu, Y., & Iyiola, O. S. (2020). Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2020.06.009' chicago: 'Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” Applied Numerical Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.apnum.2020.06.009.' ieee: 'Y. Shehu and O. S. Iyiola, “Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence,” Applied Numerical Mathematics, vol. 157. Elsevier, pp. 315–337, 2020.' ista: 'Shehu Y, Iyiola OS. 2020. Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence. Applied Numerical Mathematics. 157, 315–337.' mla: 'Shehu, Yekini, and Olaniyi S. Iyiola. “Projection Methods with Alternating Inertial Steps for Variational Inequalities: Weak and Linear Convergence.” Applied Numerical Mathematics, vol. 157, Elsevier, 2020, pp. 315–37, doi:10.1016/j.apnum.2020.06.009.' short: Y. Shehu, O.S. Iyiola, Applied Numerical Mathematics 157 (2020) 315–337. date_created: 2020-07-02T09:02:33Z date_published: 2020-11-01T00:00:00Z date_updated: 2023-08-22T07:50:43Z day: '01' ddc: - '510' department: - _id: VlKo doi: 10.1016/j.apnum.2020.06.009 ec_funded: 1 external_id: isi: - '000564648400018' file: - access_level: open_access checksum: 87d81324a62c82baa925c009dfcb0200 content_type: application/pdf creator: dernst date_created: 2020-07-02T09:08:59Z date_updated: 2020-07-14T12:48:09Z file_id: '8078' file_name: 2020_AppliedNumericalMath_Shehu.pdf file_size: 2874203 relation: main_file file_date_updated: 2020-07-14T12:48:09Z has_accepted_license: '1' intvolume: ' 157' isi: 1 language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 315-337 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Applied Numerical Mathematics publication_identifier: issn: - 0168-9274 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: 'Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence' type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 157 year: '2020' ... --- _id: '7161' abstract: - lang: eng text: In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature. acknowledgement: We are grateful to the anonymous referees and editor whose insightful comments helped to considerably improve an earlier version of this paper. The research of the first author is supported by an ERC Grant from the Institute of Science and Technology (IST). article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Aviv full_name: Gibali, Aviv last_name: Gibali - first_name: Simone full_name: Sagratella, Simone last_name: Sagratella citation: ama: Shehu Y, Gibali A, Sagratella S. Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. 2020;184:877–894. doi:10.1007/s10957-019-01616-6 apa: Shehu, Y., Gibali, A., & Sagratella, S. (2020). Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. Springer Nature. https://doi.org/10.1007/s10957-019-01616-6 chicago: Shehu, Yekini, Aviv Gibali, and Simone Sagratella. “Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” Journal of Optimization Theory and Applications. Springer Nature, 2020. https://doi.org/10.1007/s10957-019-01616-6. ieee: Y. Shehu, A. Gibali, and S. Sagratella, “Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces,” Journal of Optimization Theory and Applications, vol. 184. Springer Nature, pp. 877–894, 2020. ista: Shehu Y, Gibali A, Sagratella S. 2020. Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces. Journal of Optimization Theory and Applications. 184, 877–894. mla: Shehu, Yekini, et al. “Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces.” Journal of Optimization Theory and Applications, vol. 184, Springer Nature, 2020, pp. 877–894, doi:10.1007/s10957-019-01616-6. short: Y. Shehu, A. Gibali, S. Sagratella, Journal of Optimization Theory and Applications 184 (2020) 877–894. date_created: 2019-12-09T21:33:44Z date_published: 2020-03-01T00:00:00Z date_updated: 2023-09-06T11:27:15Z day: '01' ddc: - '518' - '510' - '515' department: - _id: VlKo doi: 10.1007/s10957-019-01616-6 ec_funded: 1 external_id: isi: - '000511805200009' file: - access_level: open_access checksum: 9f6dc6c6bf2b48cb3a2091a9ed5feaf2 content_type: application/pdf creator: dernst date_created: 2020-10-12T10:40:27Z date_updated: 2021-03-16T23:30:04Z embargo: 2021-03-15 file_id: '8647' file_name: 2020_JourOptimizationTheoryApplic_Shehu.pdf file_size: 332641 relation: main_file file_date_updated: 2021-03-16T23:30:04Z has_accepted_license: '1' intvolume: ' 184' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 877–894 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Journal of Optimization Theory and Applications publication_identifier: eissn: - 1573-2878 issn: - 0022-3239 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 184 year: '2020' ... --- _id: '6596' abstract: - lang: eng text: It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper. article_number: '138' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 citation: ama: Shehu Y. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 2019;74(4). doi:10.1007/s00025-019-1061-4 apa: Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. Springer. https://doi.org/10.1007/s00025-019-1061-4 chicago: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics. Springer, 2019. https://doi.org/10.1007/s00025-019-1061-4. ieee: Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces,” Results in Mathematics, vol. 74, no. 4. Springer, 2019. ista: Shehu Y. 2019. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138. mla: Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics, vol. 74, no. 4, 138, Springer, 2019, doi:10.1007/s00025-019-1061-4. short: Y. Shehu, Results in Mathematics 74 (2019). date_created: 2019-06-29T10:11:30Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-08-28T12:26:22Z day: '01' ddc: - '000' department: - _id: VlKo doi: 10.1007/s00025-019-1061-4 ec_funded: 1 external_id: arxiv: - '2101.09068' isi: - '000473237500002' file: - access_level: open_access checksum: c6d18cb1e16fc0c36a0e0f30b4ebbc2d content_type: application/pdf creator: kschuh date_created: 2019-07-03T15:20:40Z date_updated: 2020-07-14T12:47:34Z file_id: '6605' file_name: Springer_2019_Shehu.pdf file_size: 466942 relation: main_file file_date_updated: 2020-07-14T12:47:34Z has_accepted_license: '1' intvolume: ' 74' isi: 1 issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Results in Mathematics publication_identifier: eissn: - 1420-9012 issn: - 1422-6383 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 74 year: '2019' ... --- _id: '7000' abstract: - lang: eng text: The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps. article_number: '161' article_processing_charge: No article_type: original author: - first_name: Yekini full_name: Shehu, Yekini id: 3FC7CB58-F248-11E8-B48F-1D18A9856A87 last_name: Shehu orcid: 0000-0001-9224-7139 - first_name: Olaniyi S. full_name: Iyiola, Olaniyi S. last_name: Iyiola - first_name: Xiao-Huan full_name: Li, Xiao-Huan last_name: Li - first_name: Qiao-Li full_name: Dong, Qiao-Li last_name: Dong citation: ama: Shehu Y, Iyiola OS, Li X-H, Dong Q-L. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 2019;38(4). doi:10.1007/s40314-019-0955-9 apa: Shehu, Y., Iyiola, O. S., Li, X.-H., & Dong, Q.-L. (2019). Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. Springer Nature. https://doi.org/10.1007/s40314-019-0955-9 chicago: Shehu, Yekini, Olaniyi S. Iyiola, Xiao-Huan Li, and Qiao-Li Dong. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics. Springer Nature, 2019. https://doi.org/10.1007/s40314-019-0955-9. ieee: Y. Shehu, O. S. Iyiola, X.-H. Li, and Q.-L. Dong, “Convergence analysis of projection method for variational inequalities,” Computational and Applied Mathematics, vol. 38, no. 4. Springer Nature, 2019. ista: Shehu Y, Iyiola OS, Li X-H, Dong Q-L. 2019. Convergence analysis of projection method for variational inequalities. Computational and Applied Mathematics. 38(4), 161. mla: Shehu, Yekini, et al. “Convergence Analysis of Projection Method for Variational Inequalities.” Computational and Applied Mathematics, vol. 38, no. 4, 161, Springer Nature, 2019, doi:10.1007/s40314-019-0955-9. short: Y. Shehu, O.S. Iyiola, X.-H. Li, Q.-L. Dong, Computational and Applied Mathematics 38 (2019). date_created: 2019-11-12T12:41:44Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-08-30T07:20:32Z day: '01' ddc: - '510' - '515' - '518' department: - _id: VlKo doi: 10.1007/s40314-019-0955-9 ec_funded: 1 external_id: arxiv: - '2101.09081' isi: - '000488973100005' has_accepted_license: '1' intvolume: ' 38' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s40314-019-0955-9 month: '12' oa: 1 oa_version: Published Version project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' publication: Computational and Applied Mathematics publication_identifier: eissn: - 1807-0302 issn: - 2238-3603 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Convergence analysis of projection method for variational inequalities type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 38 year: '2019' ...