{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T11:03:06Z","timestamp":1775386986476,"version":"3.50.1"},"reference-count":59,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T00:00:00Z","timestamp":1771286400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003065","name":"Universit\u00e4t Wien","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003065","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Complexity"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.jco.2026.102029","type":"journal-article","created":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T20:03:14Z","timestamp":1771358594000},"page":"102029","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Tikhonov regularization of monotone operator flows not only ensures strong convergence of the trajectories but also speeds up the vanishing of the residuals"],"prefix":"10.1016","volume":"94","author":[{"given":"Radu Ioan","family":"Bo\u0163","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dang-Khoa","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.jco.2026.102029_br0010","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10957-013-0414-5","article-title":"Newton-like dynamics and forward\u2013backward methods for structured monotone inclusions in Hilbert spaces","volume":"161","author":"Abbas","year":"2014","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.jco.2026.102029_br0020","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s10013-017-0267-6","article-title":"Weak versus strong convergence of a regularized Newton dynamic for maximal monotone operators","volume":"46","author":"Attouch","year":"2018","journal-title":"Vietnam J. Math."},{"key":"10.1016\/j.jco.2026.102029_br0030","article-title":"Fast convex optimization via time scale and averaging of the steepest descent","author":"Attouch","year":"2024","journal-title":"Math. Oper. Res."},{"key":"10.1016\/j.jco.2026.102029_br0040","doi-asserted-by":"crossref","DOI":"10.1051\/cocv\/2025076","article-title":"Fast convex optimization via closed-loop time scaling of gradient dynamics","volume":"31","author":"Attouch","year":"2025","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0050","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10107-016-0992-8","article-title":"Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity","volume":"168","author":"Attouch","year":"2018","journal-title":"Math. Program."},{"issue":"2","key":"10.1016\/j.jco.2026.102029_br0060","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1006\/jdeq.1996.0104","article-title":"A dynamical approach to convex minimization coupling approximation with the steepest descent method","volume":"128","author":"Attouch","year":"1996","journal-title":"J. Differ. Equ."},{"issue":"10","key":"10.1016\/j.jco.2026.102029_br0070","doi-asserted-by":"crossref","first-page":"5734","DOI":"10.1016\/j.jde.2016.08.020","article-title":"Fast convex optimization via inertial dynamics with Hessian driven damping","volume":"261","author":"Attouch","year":"2016","journal-title":"J. Differ. Equ."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0080","first-page":"5","article-title":"Une remarque sur Ie comportement asymptotique des semigroupes non lin\u00e9aires","volume":"2","author":"Baillon","year":"1976","journal-title":"Houst. J. Math."},{"key":"10.1016\/j.jco.2026.102029_br0090","series-title":"Theory and Applications of Nonlinear Operators of Accretive and Monotone Types","first-page":"51","article-title":"The rate of asymptotic regularity is o(1\/n)","volume":"vol. 178","author":"Baillon","year":"1996"},{"key":"10.1016\/j.jco.2026.102029_br0100","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-48311-5","article-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"Bauschke","year":"2017"},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0110","doi-asserted-by":"crossref","first-page":"21","DOI":"10.4153\/CMB-1992-003-0","article-title":"Krasnoselski-Mann iterations in normed spaces","volume":"35","author":"Borwein","year":"1992","journal-title":"Can. Math. Bull."},{"key":"10.1016\/j.jco.2026.102029_br0120","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10884-015-9438-x","article-title":"A dynamical system associated with the fixed points set of a nonexpansive operator","volume":"29","author":"Bo\u0163","year":"2017","journal-title":"J. Dyn. Differ. Equ."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0130","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/s10208-023-09636-5","article-title":"Fast Optimistic Gradient Descent Ascent (OGDA) method in continuous and discrete time","volume":"25","author":"Bo\u0163","year":"2025","journal-title":"Found. Comput. Math."},{"issue":"3","key":"10.1016\/j.jco.2026.102029_br0140","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/10556788.2018.1457151","article-title":"Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces","volume":"34","author":"Bo\u0163","year":"2019","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0150","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1515\/anona-2020-0143","article-title":"Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure","volume":"10","author":"Bo\u0163","year":"2021","journal-title":"Adv. Nonlinear Anal."},{"key":"10.1016\/j.jco.2026.102029_br0160","article-title":"Fast second-order dynamics with slow vanishing damping approaching the zeros of a monotone and continuous operator","author":"Bo\u0163","year":"2026","journal-title":"J. Convex Anal."},{"key":"10.1016\/j.jco.2026.102029_br0170","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2021.113589","article-title":"A strongly convergent Krasnosel'skii-Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators in Hilbert spaces","volume":"395","author":"Bo\u0163","year":"2021","journal-title":"J. Comput. Appl. Math."},{"issue":"6","key":"10.1016\/j.jco.2026.102029_br0180","doi-asserted-by":"crossref","first-page":"2813","DOI":"10.1137\/22M1504305","article-title":"Fast Krasnosel'skii-Mann algorithm with a convergence rate of the fixed point iteration of o(1\/k)","volume":"61","author":"Bo\u0163","year":"2023","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jco.2026.102029_br0190","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s11856-018-1723-z","article-title":"Sharp convergence rates for averaged nonexpansive maps","volume":"227","author":"Bravo","year":"2018","journal-title":"Isr. J. Math."},{"key":"10.1016\/j.jco.2026.102029_br0200","article-title":"Op\u00e9rateurs Maximaux Monotones dans les Espaces de Hilbert et \u00c9quations d'\u00c9volution","volume":"vol. 5","author":"Br\u00e9zis","year":"1972"},{"key":"10.1016\/j.jco.2026.102029_br0210","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1090\/S0002-9904-1966-11544-6","article-title":"The solution by iteration of nonlinear functional equations in Banach spaces","volume":"72","author":"Browder","year":"1966","journal-title":"Bull. Am. Math. Soc."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0220","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.jmaa.2005.05.023","article-title":"Iterative approximation of fixed points of nonexpansive mappings","volume":"318","author":"Chidume","year":"2006","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.jco.2026.102029_br0230","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s10107-022-01830-7","article-title":"Optimal error bounds for nonexpansive fixed-point iterations in normed spaces","volume":"199","author":"Contreras","year":"2023","journal-title":"Math. Program."},{"issue":"12","key":"10.1016\/j.jco.2026.102029_br0240","doi-asserted-by":"crossref","first-page":"3753","DOI":"10.1016\/j.jde.2008.08.007","article-title":"Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization","volume":"245","author":"Cominetti","year":"2008","journal-title":"J. Differ. Equ."},{"issue":"2","key":"10.1016\/j.jco.2026.102029_br0250","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1007\/s11856-013-0045-4","article-title":"On the rate of convergence of Krasnosel'ski\u012d-Mann iterations and their connection with sums of Bernoullis","volume":"199","author":"Cominetti","year":"2014","journal-title":"Isr. J. Math."},{"key":"10.1016\/j.jco.2026.102029_br0260","author":"Csetnek"},{"key":"10.1016\/j.jco.2026.102029_br0270","series-title":"Splitting Methods in Communication, Imaging, Science, and Engineering","first-page":"115","article-title":"Convergence rate analysis of several splitting schemes","author":"Davis","year":"2016"},{"key":"10.1016\/j.jco.2026.102029_br0280","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-91654-1","article-title":"The Krasnosel'ski\u012d-Mann Iterative Method: Recent Progress and Applications","author":"Dong","year":"2022"},{"key":"10.1016\/j.jco.2026.102029_br0290","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0022-247X(72)90056-X","article-title":"A note on segmenting Mann iterates","volume":"40","author":"Groetsch","year":"1972","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"10.1016\/j.jco.2026.102029_br0300","doi-asserted-by":"crossref","first-page":"292","DOI":"10.2307\/1967124","article-title":"Note on the derivatives with respect to a parameter of the solutions of a system of differential equations","volume":"20","author":"Gronwall","year":"1919","journal-title":"Ann. Math."},{"issue":"3","key":"10.1016\/j.jco.2026.102029_br0310","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1137\/19M1299049","article-title":"Tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems","volume":"30","author":"Gu","year":"2020","journal-title":"SIAM J. Optim."},{"issue":"6","key":"10.1016\/j.jco.2026.102029_br0320","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1090\/S0002-9904-1967-11864-0","article-title":"Fixed points of nonexpanding maps","volume":"73","author":"Halpern","year":"1967","journal-title":"Bull. Am. Math. Soc."},{"key":"10.1016\/j.jco.2026.102029_br0330","article-title":"Syst\u00e9mes Dynamiques Dissipatifs et Applications","volume":"vol. 17","author":"Haraux","year":"1991"},{"key":"10.1016\/j.jco.2026.102029_br0340","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1090\/mcom\/3851","article-title":"Convergence analysis of the Halpern iteration with adaptive anchoring parameters","volume":"93","author":"He","year":"2024","journal-title":"Math. Comput."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0350","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1090\/S0002-9939-1976-0412909-X","article-title":"Fixed points and iteration of a nonexpansive mapping in a Banach space","volume":"59","author":"Ishikawa","year":"1976","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0360","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0022-247X(81)90245-6","article-title":"Asymptotic behavior of solutions of a nonlinear evolution equation","volume":"83","author":"Israel","year":"1981","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.jco.2026.102029_br0370","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10107-021-01643-0","article-title":"Accelerated proximal point method for maximally monotone operators","volume":"190","author":"Kim","year":"2021","journal-title":"Math. Program."},{"key":"10.1016\/j.jco.2026.102029_br0380","first-page":"123","article-title":"Two remarks on the method of successive approximations","volume":"10","author":"Krasnosel'ski\u012d","year":"1955","journal-title":"Usp. Mat. Nauk"},{"key":"10.1016\/j.jco.2026.102029_br0390","article-title":"Fast extra gradient methods for smooth structured nonconvex-nonconcave minimax problems","volume":"34","author":"Lee","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"1\u20132","key":"10.1016\/j.jco.2026.102029_br0400","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s10107-015-0964-4","article-title":"Convergence rates with inexact non-expansive operators","volume":"159","author":"Liang","year":"2016","journal-title":"Math. Program."},{"issue":"2","key":"10.1016\/j.jco.2026.102029_br0410","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s11590-020-01617-9","article-title":"On the convergence rate of the Halpern-iteration","volume":"15","author":"Lieder","year":"2021","journal-title":"Optim. Lett."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0420","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1017\/S000497271600109X","article-title":"On the convergence rate of the Krasnosel'ski\u012d-Mann iteration","volume":"96","author":"Matsushita","year":"2017","journal-title":"Bull. Aust. Math. Soc."},{"issue":"10","key":"10.1016\/j.jco.2026.102029_br0430","first-page":"1","article-title":"Inertial Krasnoselskii-Mann iterations","volume":"32","author":"Maul\u00e9n","year":"2024","journal-title":"Set-Valued Var. Anal."},{"key":"10.1016\/j.jco.2026.102029_br0440","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1090\/S0002-9904-1967-11761-0","article-title":"Weak convergence of the sequence of successive approximations for nonexpansive mappings","volume":"73","author":"Opial","year":"1967","journal-title":"Bull. Am. Math. Soc."},{"key":"10.1016\/j.jco.2026.102029_br0450","series-title":"Proceedings of the 39th International Conference on Machine Learning","article-title":"Exact optimal accelerated complexity for fixed-point iterations","volume":"vol. 162","author":"Park","year":"2022"},{"key":"10.1016\/j.jco.2026.102029_br0460","article-title":"Introduction to Optimization","author":"Polyak","year":"1987"},{"issue":"15","key":"10.1016\/j.jco.2026.102029_br0470","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1080\/01630563.2021.2001826","article-title":"Convergence of Halpern's iteration method with applications in optimization","volume":"42","author":"Qi","year":"2021","journal-title":"Numer. Funct. Anal. Optim."},{"key":"10.1016\/j.jco.2026.102029_br0480","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/0022-247X(79)90024-6","article-title":"Weak convergence theorems for nonexpansive mappings in Banach spaces","volume":"67","author":"Reich","year":"1979","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"10.1016\/j.jco.2026.102029_br0490","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1137\/16M105592X","article-title":"A first order method for solving convex bilevel optimization problems","volume":"27","author":"Sabach","year":"2017","journal-title":"SIAM J. Optim."},{"issue":"153","key":"10.1016\/j.jco.2026.102029_br0500","first-page":"1","article-title":"A differential equation for modeling Nesterov's accelerated gradient method: theory and insights","volume":"17","author":"Su","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.jco.2026.102029_br0510","article-title":"Continuous-Time Analysis of Anchor Acceleration","volume":"vol. 36","author":"Suh","year":"2023"},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0520","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1155\/FPTA.2005.103","article-title":"Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces","volume":"2005","author":"Suzuki","year":"2005","journal-title":"Fixed Point Theory Appl."},{"issue":"01","key":"10.1016\/j.jco.2026.102029_br0530","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1090\/S0002-9939-06-08435-8","article-title":"A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings","volume":"135","author":"Suzuki","year":"2006","journal-title":"Proc. Am. Math. Soc."},{"key":"10.1016\/j.jco.2026.102029_br0540","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s10589-023-00518-8","article-title":"From Halpern's fixed-point iterations to Nesterov's accelerated interpretations for root-finding problems","volume":"87","author":"Tran-Dinh","year":"2024","journal-title":"Comput. Optim. Appl."},{"key":"10.1016\/j.jco.2026.102029_br0550","author":"Tran-Dinh"},{"issue":"5","key":"10.1016\/j.jco.2026.102029_br0560","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1007\/BF01190119","article-title":"Approximation of fixed points of nonexpansive mappings","volume":"58","author":"Wittmann","year":"1992","journal-title":"Arch. Math."},{"issue":"1","key":"10.1016\/j.jco.2026.102029_br0570","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1112\/S0024610702003332","article-title":"Iterative algorithms for nonlinear operators","volume":"66","author":"Xu","year":"2002","journal-title":"J. Lond. Math. Soc."},{"issue":"3","key":"10.1016\/j.jco.2026.102029_br0580","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1023\/A:1023073621589","article-title":"An iterative approach to quadratic optimization","volume":"116","author":"Xu","year":"2003","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.jco.2026.102029_br0590","series-title":"Proceedings of the 38th International Conference on Machine Learning","first-page":"12098","article-title":"Accelerated algorithms for smooth convex-concave minimax problems with O(1\/k2) rate on squared gradient norm","volume":"vol. 139","author":"Yoon","year":"2021"}],"container-title":["Journal of Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X26000142?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X26000142?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T10:24:49Z","timestamp":1775384689000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0885064X26000142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":59,"alternative-id":["S0885064X26000142"],"URL":"https:\/\/doi.org\/10.1016\/j.jco.2026.102029","relation":{},"ISSN":["0885-064X"],"issn-type":[{"value":"0885-064X","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Tikhonov regularization of monotone operator flows not only ensures strong convergence of the trajectories but also speeds up the vanishing of the residuals","name":"articletitle","label":"Article Title"},{"value":"Journal of Complexity","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jco.2026.102029","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"102029"}}