{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T05:27:51Z","timestamp":1735882071114,"version":"3.32.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T00:00:00Z","timestamp":1709510400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T00:00:00Z","timestamp":1709510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Scientific Research Project of Tianjin Municipal Education Commission","award":["2022ZD007"],"award-info":[{"award-number":["2022ZD007"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1007\/s11075-024-01788-x","type":"journal-article","created":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T06:02:20Z","timestamp":1709532140000},"page":"133-163","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inertial self-adaptive algorithms for solving non-smooth convex optimization problems"],"prefix":"10.1007","volume":"98","author":[{"given":"Xin","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peichao","family":"Duan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,4]]},"reference":[{"key":"1788_CR1","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"1788_CR2","volume-title":"Operateurs Maximaux Monotones","author":"H Brezis","year":"1973","unstructured":"Brezis, H.: Operateurs Maximaux Monotones. North-Holland Mathematics Studies, Amsterdam-London (1973)"},{"key":"1788_CR3","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1088\/0266-5611\/18\/2\/310","volume":"18","author":"C Byrne","year":"2002","unstructured":"Byrne, C.: Iterative oblique projection onto convex subsets and the split feasibility problem. Inverse Probl. 18, 441\u2013453 (2002)","journal-title":"Inverse Probl."},{"key":"1788_CR4","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s10915-021-01608-7","volume":"88","author":"P Cholamjiak","year":"2021","unstructured":"Cholamjiak, P., Hieu, D.V., Cho, Y.J.: Relaxed forward-backward splitting methods for solving variational inclusions and applications. J. Sci. Comput. 88, 85 (2021)","journal-title":"J. Sci. Comput."},{"key":"1788_CR5","doi-asserted-by":"crossref","unstructured":"Duan, P.C., Zhang, Y.Q.: Alternated and multi-step inertial approximation methods for solving convex bilevel optimization problems. Optimization 72(10), 2517\u20132545 (2023)","DOI":"10.1080\/02331934.2022.2069022"},{"key":"1788_CR6","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1186\/s13660-020-02522-6","volume":"2020","author":"PC Duan","year":"2020","unstructured":"Duan, P.C., Zhang, Y.Q., Bu, Q.X.: New inertial proximal gradient methods for unconstrained convex optimization problems. J. Inequal. Appl. 2020, 255 (2020)","journal-title":"J. Inequal. Appl."},{"key":"1788_CR7","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/942315","volume":"2013","author":"SN He","year":"2013","unstructured":"He, S.N., Yang, C.P.: Solving the variational inequality problem defined on intersection of finite level sets. Abstr. Appl. Anal. 2013, 942315 (2013)","journal-title":"Abstr. Appl. Anal."},{"key":"1788_CR8","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1080\/10556788.2017.1396601","volume":"34","author":"F Iutzeler","year":"2019","unstructured":"Iutzeler, F., Hendricks, M.: A generic online acceleration scheme for optimization algorithms via relaxation and inertia. Optim. Methods Softw. 34, 383\u2013405 (2019)","journal-title":"Optim. Methods Softw."},{"key":"1788_CR9","doi-asserted-by":"publisher","first-page":"688","DOI":"10.1007\/s10957-018-1226-4","volume":"176","author":"F Iutzeler","year":"2018","unstructured":"Iutzeler, F., Malick, J.: On the proximal gradient algorithm with alternated inertia. Optim. Theory Appl. 176, 688\u2013710 (2018)","journal-title":"Optim. Theory Appl."},{"issue":"4","key":"1788_CR10","first-page":"412","volume":"5","author":"S Kesornprom","year":"2022","unstructured":"Kesornprom, S., Cholamjiak, P.: A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification. Adv. Nonlinear Anal. 5(4), 412\u2013422 (2022)","journal-title":"Adv. Nonlinear Anal."},{"key":"1788_CR11","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s40314-022-02042-7","volume":"41","author":"S Kesornprom","year":"2022","unstructured":"Kesornprom, S., Cholamjiak, P., Park, C.: New proximal type algorithms for convex minimization and its application to image deblurring. Computational and Apllied Mathematics. 41, 333 (2022)","journal-title":"Computational and Apllied Mathematics."},{"key":"1788_CR12","unstructured":"Liang, J.W.: Convergence rates of first-order operator splitting methods. Optim. Cont[math.OC]. Normandie Universit\u00e9. Greyc Cnrs Umr Bibliogr., 60\u201372 (2016)"},{"key":"1788_CR13","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/8\/085004","volume":"28","author":"G Lopez","year":"2012","unstructured":"Lopez, G., Martin-Marquez, V., Wang, F., Xu, H.K.: Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 28, 085004 (2012)","journal-title":"Inverse Probl."},{"issue":"1","key":"1788_CR14","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.jmaa.2005.05.028","volume":"318","author":"G Marino","year":"2006","unstructured":"Marino, G., Xu, H.K.: A general iterative method for nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 318(1), 43\u201352 (2006)","journal-title":"J. Math. Anal. Appl."},{"key":"1788_CR15","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1016\/j.jmaa.2006.06.055","volume":"329","author":"G Marino","year":"2007","unstructured":"Marino, G., Xu, H.K.: Weak and strong convergence theorems for strict peseudo-contractions in Hilbert spaces. J. Math. Anal. Appl. 329, 336\u2013346 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"1788_CR16","unstructured":"Moreau, J.J.: Proprietes des applications \u2019prox\u2019. C.R. Acad. Sci. Paris S\u00e9r. A Math. 256, 1069\u20131071 (1963)"},{"key":"1788_CR17","doi-asserted-by":"publisher","first-page":"2099","DOI":"10.1007\/s11590-013-0708-4","volume":"8","author":"A Moudafi","year":"2014","unstructured":"Moudafi, A., Thakur, B.S.: Solving proximal split feasibility problems without prior knowledge of operator norm. Optim. Lett. 8, 2099\u20132110 (2014)","journal-title":"Optim. Lett."},{"key":"1788_CR18","first-page":"543","volume":"269","author":"Y Nesterov","year":"1983","unstructured":"Nesterov, Y.: A method for solving the convex programming problem with convergence rate $$O(1\/k^2)$$. Dokl. Akad. Nauk SSSR 269, 543\u2013547 (1983)","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"1","key":"1788_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10092-018-0300-5","volume":"56","author":"Y Shehu","year":"2019","unstructured":"Shehu, Y., Cholamjiak, P.: Iterative method with inertial for variational inequalities in Hilbert spaces. Calcolo 56(1), 1\u201321 (2019)","journal-title":"Calcolo"},{"key":"1788_CR20","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 mappings. SIAM J. Control. Optim. 38, 431\u2013446 (2000)","journal-title":"SIAM J. Control. Optim."},{"issue":"3","key":"1788_CR21","first-page":"1","volume":"35B","author":"HK Xu","year":"2014","unstructured":"Xu, H.K.: Properties and iterative methods for the lasso and its variants. Chin. Ann. Math. 35B(3), 1\u201318 (2014)","journal-title":"Chin. Ann. Math."},{"key":"1788_CR22","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1186\/s13663-015-0462-7","volume":"2015","author":"Y Yao","year":"2015","unstructured":"Yao, Y., Yao, Z., Abdou, A.A., et al.: Self-adaptive algorithms for proximal split feasibility problems and strong convergence analysis. Fixed Point Theory Appl. 2015, 205 (2015)","journal-title":"Fixed Point Theory Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01788-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01788-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01788-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T16:57:42Z","timestamp":1735837062000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01788-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,4]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["1788"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01788-x","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2024,3,4]]},"assertion":[{"value":"7 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 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":"Not applicable","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}