{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T22:31:11Z","timestamp":1784241071079,"version":"3.55.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T00:00:00Z","timestamp":1722556800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T00:00:00Z","timestamp":1722556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s10957-024-02501-7","type":"journal-article","created":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T14:05:57Z","timestamp":1722607557000},"page":"256-284","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity"],"prefix":"10.1007","volume":"203","author":[{"given":"Yu","family":"Cao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanheng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Habib","family":"ur Rehman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yekini","family":"Shehu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jen-Chih","family":"Yao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,2]]},"reference":[{"key":"2501_CR1","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/s10589-021-00291-6","volume":"80","author":"FJ Arag\u00f3n Artacho","year":"2021","unstructured":"Arag\u00f3n Artacho, F.J., Campoy, R., Tam, M.K.: Strengthened splitting methods for computing resolvents. Comput. Optim. Appl. 80, 549\u2013585 (2021)","journal-title":"Comput. Optim. Appl."},{"key":"2501_CR2","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1007\/s10589-022-00400-z","volume":"86","author":"FJ Arag\u00f3n Artacho","year":"2023","unstructured":"Arag\u00f3n Artacho, F.J., Campoy, R., Tam, M.K., Torregroa-Bel\u00e9n, D.: Distributed forward-backward methods for ring networks. Comput. Optim. Appl. 86, 845\u2013870 (2023)","journal-title":"Comput. Optim. Appl."},{"key":"2501_CR3","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1080\/10556788.2018.1504049","volume":"34","author":"FJ Arag\u00f3n Artacho","year":"2019","unstructured":"Arag\u00f3n Artacho, F.J., Censor, Y., Gibali, A.: The cyclic Douglas\u2013Rachford algorithm with $$r$$-sets-Douglas\u2013Rachford operators. Optim. Methods Softw. 34, 875\u2013889 (2019)","journal-title":"Optim. Methods Softw."},{"key":"2501_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2017","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd edn. Springer, New York (2017)","edition":"2"},{"key":"2501_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10957-013-0381-x","volume":"160","author":"JM Borwein","year":"2014","unstructured":"Borwein, J.M., Tam, M.K.: A cyclic Douglas\u2013Rachford iteration scheme. J. Optim. Theory Appl. 160, 1\u201329 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"2501_CR6","doi-asserted-by":"publisher","first-page":"1239","DOI":"10.1080\/02331934.2013.855210","volume":"64","author":"LM Brice\u00f1o-Arias","year":"2015","unstructured":"Brice\u00f1o-Arias, L.M.: Forward-Douglas\u2013Rachford splitting and forward-partial inverse method for solving monotone inclusions. Optimization 64, 1239\u20131261 (2015)","journal-title":"Optimization"},{"key":"2501_CR7","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"JF Cai","year":"2010","unstructured":"Cai, J.F., Candes, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20, 1956\u20131982 (2010)","journal-title":"SIAM J. Optim."},{"key":"2501_CR8","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1109\/JSTSP.2007.910264","volume":"1","author":"PL Combettes","year":"2007","unstructured":"Combettes, P.L., Pesquet, J.C.: A Douglas\u2013Rachford splitting approach to nonsmooth convex variational signal recovery. IEEE J. Sel. Top. Signal Process. 1, 564\u2013574 (2007)","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"2501_CR9","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1007\/s11228-017-0421-z","volume":"25","author":"D Davis","year":"2019","unstructured":"Davis, D., Yin, W.T.: A three-operator splitting scheme and its optimization applications. Set-Valued Var. Anal. 25, 829\u2013858 (2019)","journal-title":"Set-Valued Var. Anal."},{"key":"2501_CR10","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1090\/S0002-9904-1964-11178-2","volume":"70","author":"AA Goldstein","year":"1964","unstructured":"Goldstein, A.A.: Convex programming in Hilbert space. Bull. Am. Math. Soc. 70, 709\u2013710 (1964)","journal-title":"Bull. Am. Math. Soc."},{"key":"2501_CR11","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"PL Lions","year":"1979","unstructured":"Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16, 964\u2013979 (1979)","journal-title":"SIAM J. Numer. Anal."},{"key":"2501_CR12","doi-asserted-by":"publisher","first-page":"1451","DOI":"10.1137\/18M1207260","volume":"30","author":"Y Malitsky","year":"2020","unstructured":"Malitsky, Y., Tam, M.K.: A forward-backward splitting method for monotone inclusions without cocoercivity. SIAM J. Optim. 30, 1451\u20131472 (2020)","journal-title":"SIAM J. Optim."},{"key":"2501_CR13","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1090\/S0002-9904-1967-11761-0","volume":"73","author":"Z Opial","year":"1967","unstructured":"Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73, 591\u2013597 (1967)","journal-title":"Bull. Am. Math. Soc."},{"key":"2501_CR14","doi-asserted-by":"publisher","first-page":"1199","DOI":"10.1137\/120872802","volume":"6","author":"H Raguet","year":"2013","unstructured":"Raguet, H., Fadili, J., Peyr\u00e9, G.: A generalized forward-backward splitting. SIAM J. Imag. Sci. 6, 1199\u20131226 (2013)","journal-title":"SIAM J. Imag. Sci."},{"key":"2501_CR15","first-page":"125248","volume":"381","author":"J Rieger","year":"2020","unstructured":"Rieger, J., Tam, M.K.: Backward-forward-reflected-backward splitting for three operator monotone inclusion. Appl. Math. Comput. 381, 125248 (2020)","journal-title":"Appl. Math. Comput."},{"key":"2501_CR16","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s10107-019-01403-1","volume":"182","author":"EK Ryu","year":"2020","unstructured":"Ryu, E.K.: Uniqueness of DRS as the 2 oprator resolvent-splitting and impossibility of 3 operator resolvent-splitting. Math. Program. 182, 233\u2013273 (2020)","journal-title":"Math. Program."},{"key":"2501_CR17","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1137\/S0363012998338806","volume":"38","author":"P Tseng","year":"2000","unstructured":"Tseng, P.: A modified forward-backward splitting method for maximal monotone mapping. SIAM J. Control. Optim. 38, 431\u2013446 (2000)","journal-title":"SIAM J. Control. Optim."},{"key":"2501_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-023-00677-0","author":"CX Zong","year":"2023","unstructured":"Zong, C.X., Tang, Y.C., Zhang, G.F.: Solving monotone inclusions involving the sum of three maximally monotone operators and cocoercive operator with applications. Set-Val. Var. Anal. (2023). https:\/\/doi.org\/10.1007\/s11228-023-00677-0","journal-title":"Set-Val. Var. Anal."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02501-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-024-02501-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-024-02501-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T18:04:49Z","timestamp":1730484289000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-024-02501-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,2]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["2501"],"URL":"https:\/\/doi.org\/10.1007\/s10957-024-02501-7","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,2]]},"assertion":[{"value":"3 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"All the authors gave consent for the publication of identifiable details to be published in the journal and article.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"All the authors gave the ethical approval and consent to participate in this article.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval and Consent to participate"}}]}}