{"month":"05","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."}],"language":[{"iso":"eng"}],"isi":1,"scopus_import":"1","citation":{"chicago":"Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” <i>Numerical Algorithms</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11075-019-00758-y\">https://doi.org/10.1007/s11075-019-00758-y</a>.","short":"Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.","ama":"Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. <i>Numerical Algorithms</i>. 2020;84:365-388. doi:<a href=\"https://doi.org/10.1007/s11075-019-00758-y\">10.1007/s11075-019-00758-y</a>","ieee":"Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for monotone variational inequalities in Hilbert spaces,” <i>Numerical Algorithms</i>, 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.","apa":"Shehu, Y., Li, X.-H., &#38; Dong, Q.-L. (2020). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. <i>Numerical Algorithms</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11075-019-00758-y\">https://doi.org/10.1007/s11075-019-00758-y</a>","mla":"Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” <i>Numerical Algorithms</i>, vol. 84, Springer Nature, 2020, pp. 365–88, doi:<a href=\"https://doi.org/10.1007/s11075-019-00758-y\">10.1007/s11075-019-00758-y</a>."},"date_updated":"2023-08-17T13:51:18Z","day":"01","external_id":{"isi":["000528979000015"]},"acknowledgement":"The research of this author is supported by the ERC grant at the IST.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","has_accepted_license":"1","date_published":"2020-05-01T00:00:00Z","oa":1,"year":"2020","file_date_updated":"2020-07-14T12:47:34Z","_id":"6593","ddc":["000"],"article_type":"original","project":[{"grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"publication_identifier":{"eissn":["1572-9265"],"issn":["1017-1398"]},"status":"public","department":[{"_id":"VlKo"}],"publisher":"Springer Nature","intvolume":"        84","author":[{"full_name":"Shehu, Yekini","first_name":"Yekini","last_name":"Shehu","id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139"},{"full_name":"Li, Xiao-Huan","first_name":"Xiao-Huan","last_name":"Li"},{"full_name":"Dong, Qiao-Li","first_name":"Qiao-Li","last_name":"Dong"}],"doi":"10.1007/s11075-019-00758-y","type":"journal_article","title":"An efficient projection-type method for monotone variational inequalities in Hilbert spaces","date_created":"2019-06-27T20:09:33Z","page":"365-388","ec_funded":1,"quality_controlled":"1","oa_version":"Submitted Version","file":[{"file_id":"6927","date_created":"2019-10-01T13:14:10Z","checksum":"bb1a1eb3ebb2df380863d0db594673ba","content_type":"application/pdf","file_size":359654,"date_updated":"2020-07-14T12:47:34Z","file_name":"ExtragradientMethodPaper.pdf","relation":"main_file","creator":"kschuh","access_level":"open_access"}],"volume":84,"article_processing_charge":"No","publication":"Numerical Algorithms"}