{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T22:12:46Z","timestamp":1778710366982,"version":"3.51.4"},"reference-count":34,"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":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFA0714300"],"award-info":[{"award-number":["2020YFA0714300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62576098"],"award-info":[{"award-number":["62576098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62473098"],"award-info":[{"award-number":["62473098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Automatica"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.automatica.2026.112965","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T16:23:43Z","timestamp":1775147023000},"page":"112965","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Local Adapt-Then-Combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration"],"prefix":"10.1016","volume":"188","author":[{"given":"Luyao","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinli","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenying","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinde","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"11","key":"10.1016\/j.automatica.2026.112965_b1","doi-asserted-by":"crossref","first-page":"7371","DOI":"10.1109\/TAC.2024.3383271","article-title":"Local exact-diffusion for decentralized optimization and learning","volume":"69","author":"Alghunaim","year":"2024","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"6","key":"10.1016\/j.automatica.2026.112965_b2","doi-asserted-by":"crossref","first-page":"2787","DOI":"10.1109\/TAC.2020.3009363","article-title":"Decentralized proximal gradient algorithms with linear convergence rates","volume":"66","author":"Alghunaim","year":"2020","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112965_b3","series-title":"Convex optimization algorithms","author":"Bertsekas","year":"2015"},{"issue":"3","key":"10.1016\/j.automatica.2026.112965_b4","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1145\/1961189.1961199","article-title":"LIBSVM: A library for support vector machines","volume":"2","author":"Chang","year":"2011","journal-title":"ACM Transactions on Intelligent Systems and Technology"},{"issue":"4","key":"10.1016\/j.automatica.2026.112965_b5","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/050626090","article-title":"Signal recovery by proximal forward-backward splitting","volume":"4","author":"Combettes","year":"2005","journal-title":"Multiscale Modeling & Simulation"},{"key":"10.1016\/j.automatica.2026.112965_b6","unstructured":"Condat,\u00a0L., & Richt\u00e1rik,\u00a0P. (2023). RandProx: Primal-dual optimization algorithms with randomized proximal updates. In International conference on learning representations."},{"key":"10.1016\/j.automatica.2026.112965_b7","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1109\/TSP.2023.3250839","article-title":"Decentralized inexact proximal gradient method with network-independent stepsizes for convex composite optimization","volume":"71","author":"Guo","year":"2023","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"5","key":"10.1016\/j.automatica.2026.112965_b8","doi-asserted-by":"crossref","first-page":"2995","DOI":"10.1109\/TAC.2023.3301289","article-title":"DISA: A dual inexact splitting algorithm for distributed convex composite optimization","volume":"69","author":"Guo","year":"2024","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.automatica.2026.112965_b9","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1109\/TSIPN.2025.3600766","article-title":"A proximal gradient method with probabilistic multi-gossip communications for decentralized composite optimization","volume":"11","author":"Guo","year":"2025","journal-title":"IEEE Transactions on Signal and Information Processing over Networks"},{"issue":"17","key":"10.1016\/j.automatica.2026.112965_b10","doi-asserted-by":"crossref","first-page":"4494","DOI":"10.1109\/TSP.2019.2926022","article-title":"A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates","volume":"67","author":"Li","year":"2019","journal-title":"IEEE Transactions on Signal Processing"},{"key":"10.1016\/j.automatica.2026.112965_b11","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.automatica.2019.04.004","article-title":"Exponential convergence of distributed primal\u2013dual convex optimization algorithm without strong convexity","volume":"105","author":"Liang","year":"2019","journal-title":"Automatica"},{"key":"10.1016\/j.automatica.2026.112965_b12","article-title":"Decentralized gradient tracking with local steps","author":"Liu","year":"2024","journal-title":"Optimization Methods & Software"},{"key":"10.1016\/j.automatica.2026.112965_b13","series-title":"International conference on machine learning","first-page":"15750","article-title":"Proxskip: Yes! local gradient steps provably lead to communication acceleration! finally!","author":"Mishchenko","year":"2022"},{"issue":"1","key":"10.1016\/j.automatica.2026.112965_b14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2600000004","article-title":"Convergence rate of distributed averaging dynamics and optimization in networks","volume":"2","author":"Nedi\u0107","year":"2015","journal-title":"Foundations and Trends\u00ae in Systems and Control"},{"issue":"5","key":"10.1016\/j.automatica.2026.112965_b15","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/JPROC.2018.2817461","article-title":"Network topology and communication-computation tradeoffs in decentralized optimization","volume":"106","author":"Nedi\u0107","year":"2018","journal-title":"Proceedings of the IEEE"},{"issue":"4","key":"10.1016\/j.automatica.2026.112965_b16","doi-asserted-by":"crossref","first-page":"2597","DOI":"10.1137\/16M1084316","article-title":"Achieving geometric convergence for distributed optimization over time-varying graphs","volume":"27","author":"Nedic","year":"2017","journal-title":"SIAM Journal on Optimization"},{"key":"10.1016\/j.automatica.2026.112965_b17","series-title":"American control conference","first-page":"3950","article-title":"Geometrically convergent distributed optimization with uncoordinated step-sizes","author":"Nedi\u0107","year":"2017"},{"issue":"1","key":"10.1016\/j.automatica.2026.112965_b18","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/TAC.2008.2009515","article-title":"Distributed subgradient methods for multi-agent optimization","volume":"54","author":"Nedi\u0107","year":"2009","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"10.1016\/j.automatica.2026.112965_b19","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s10107-012-0629-5","article-title":"Gradient methods for minimizing composite functions","volume":"140","author":"Nesterov","year":"2013","journal-title":"Mathematical Programming"},{"key":"10.1016\/j.automatica.2026.112965_b20","series-title":"IEEE conference on decision and control","first-page":"4309","article-title":"On the performance of gradient tracking with local updates","author":"Nguyen","year":"2023"},{"issue":"3","key":"10.1016\/j.automatica.2026.112965_b21","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1109\/TCNS.2017.2698261","article-title":"Harnessing smoothness to accelerate distributed optimization","volume":"5","author":"Qu","year":"2017","journal-title":"IEEE Transactions on Control of Network Systems"},{"key":"10.1016\/j.automatica.2026.112965_b22","first-page":"233","article-title":"A convergence theorem for nonnegative almost supermartingales and some applications","author":"Robbins","year":"1971","journal-title":"Optimizing Methods in Statistics"},{"key":"10.1016\/j.automatica.2026.112965_b23","series-title":"International conference on machine learning","first-page":"3027","article-title":"Optimal algorithms for smooth and strongly convex distributed optimization in networks","author":"Scaman","year":"2017"},{"issue":"2","key":"10.1016\/j.automatica.2026.112965_b24","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1137\/14096668X","article-title":"EXTRA: An exact first-order algorithm for decentralized consensus optimization","volume":"25","author":"Shi","year":"2015","journal-title":"SIAM Journal on Optimization"},{"issue":"22","key":"10.1016\/j.automatica.2026.112965_b25","doi-asserted-by":"crossref","first-page":"6013","DOI":"10.1109\/TSP.2015.2461520","article-title":"A proximal gradient algorithm for decentralized composite optimization","volume":"63","author":"Shi","year":"2015","journal-title":"IEEE Transactions on Signal Processing"},{"key":"10.1016\/j.automatica.2026.112965_b26","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.automatica.2018.04.010","article-title":"Augmented Lagrange algorithms for distributed optimization over multi-agent networks via edge-based method","volume":"94","author":"Shi","year":"2018","journal-title":"Automatica"},{"issue":"1","key":"10.1016\/j.automatica.2026.112965_b27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-023-01997-7","article-title":"Optimal gradient tracking for decentralized optimization","volume":"207","author":"Song","year":"2024","journal-title":"Mathematical Programming"},{"issue":"2","key":"10.1016\/j.automatica.2026.112965_b28","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1137\/19M1259973","article-title":"Distributed optimization based on gradient tracking revisited: Enhancing convergence rate via surrogation","volume":"32","author":"Sun","year":"2022","journal-title":"SIAM Journal on Optimization"},{"key":"10.1016\/j.automatica.2026.112965_b29","series-title":"International conference on machine learning","first-page":"4848","article-title":"D2: Decentralized training over decentralized data","author":"Tang","year":"2018"},{"key":"10.1016\/j.automatica.2026.112965_b30","doi-asserted-by":"crossref","first-page":"3555","DOI":"10.1109\/TSP.2021.3086579","article-title":"Distributed algorithms for composite optimization: Unified framework and convergence analysis","volume":"69","author":"Xu","year":"2021","journal-title":"IEEE Transactions on Signal Processing"},{"key":"10.1016\/j.automatica.2026.112965_b31","series-title":"IEEE conference on decision and control","first-page":"2055","article-title":"Augmented distributed gradient methods for multi-agent optimization under uncoordinated constant stepsizes","author":"Xu","year":"2015"},{"issue":"280","key":"10.1016\/j.automatica.2026.112965_b32","first-page":"1","article-title":"Removing data heterogeneity influence enhances network topology dependence of decentralized SGD","volume":"24","author":"Yuan","year":"2023","journal-title":"Journal of Machine Learning Research"},{"issue":"3","key":"10.1016\/j.automatica.2026.112965_b33","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1137\/130943170","article-title":"On the convergence of decentralized gradient descent","volume":"26","author":"Yuan","year":"2016","journal-title":"SIAM Journal on Optimization"},{"issue":"3","key":"10.1016\/j.automatica.2026.112965_b34","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1109\/TSP.2018.2875898","article-title":"Exact diffusion for distributed optimization and learning\u2014Part I: Algorithm development","volume":"67","author":"Yuan","year":"2018","journal-title":"IEEE Transactions on Signal Processing"}],"container-title":["Automatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0005109826001494?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0005109826001494?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T21:57:45Z","timestamp":1778709465000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0005109826001494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":34,"alternative-id":["S0005109826001494"],"URL":"https:\/\/doi.org\/10.1016\/j.automatica.2026.112965","relation":{},"ISSN":["0005-1098"],"issn-type":[{"value":"0005-1098","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Local Adapt-Then-Combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration","name":"articletitle","label":"Article Title"},{"value":"Automatica","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.automatica.2026.112965","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"112965"}}