{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T10:20:25Z","timestamp":1768558825659,"version":"3.49.0"},"reference-count":44,"publisher":"Informa UK Limited","issue":"1","funder":[{"name":"National key research and development program of China","award":["2021YFA1000403"],"award-info":[{"award-number":["2021YFA1000403"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11731013, 11991022, U19B2040"],"award-info":[{"award-number":["11731013, 11991022, U19B2040"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Optimization Methods and Software"],"published-print":{"date-parts":[[2023,1,2]]},"DOI":"10.1080\/10556788.2022.2091562","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T15:17:18Z","timestamp":1658243838000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":2,"title":["On inexact stochastic splitting methods for a class of nonconvex composite optimization problems with relative error"],"prefix":"10.1080","volume":"38","author":[{"given":"Jia","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China"}]},{"given":"Congying","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China"},{"name":"Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, People's Republic of China"}]},{"given":"Tiande","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China"},{"name":"Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, People's Republic of China"}]},{"given":"Tong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China"},{"name":"Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, People's Republic of China"}]}],"member":"301","published-online":{"date-parts":[[2022,7,19]]},"reference":[{"key":"CIT0001","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-020-00191-1"},{"key":"CIT0002","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0484-9"},{"key":"CIT0003","unstructured":"R. Babanezhad, M.O. Ahmed, A. Virani, M. Schmidt, J. Kone\u010dn y`, and S. Sallinen, Stop wasting my gradients: Practical SVRG, in Advances in Neural Information Processing Systems, Curran Associates, Montr\u00e9al, QC, 2015, pp. 2251\u20132259."},{"key":"CIT0004","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-016-0376-5"},{"key":"CIT0005","unstructured":"A. Defazio, F. Bach, and S. Lacoste-Julien, SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives, in Advances in Neural Information Processing Systems, Curran Associates, Montr\u00e9al, QC, 2014, pp. 1646\u20131654."},{"key":"CIT0006","unstructured":"C. Fang, C.J. Li, Z. Lin, and T. Zhang, Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator, in Advances in Neural Information Processing Systems, Curran Associates, Montr\u00e9al, QC, 2018, pp. 689\u2013699."},{"key":"CIT0007","doi-asserted-by":"publisher","DOI":"10.1080\/00207728108963798"},{"key":"CIT0008","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(76)90003-1"},{"key":"CIT0009","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-017-0621-6"},{"key":"CIT0010","doi-asserted-by":"publisher","DOI":"10.1137\/110848864"},{"key":"CIT0011","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-014-0846-1"},{"key":"CIT0012","first-page":"41","volume":"9","author":"Glowinski R.","year":"1975","journal-title":"Revue Fr. Autom. Inform. Rech. Op\u00e9r., Anal. Num\u00e9r."},{"key":"CIT0013","doi-asserted-by":"publisher","DOI":"10.1137\/110836936"},{"key":"CIT0014","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-1034-2"},{"key":"CIT0015","doi-asserted-by":"publisher","DOI":"10.1137\/140990309"},{"key":"CIT0016","doi-asserted-by":"crossref","unstructured":"F. Huang, S. Chen, and H. Huang, Faster stochastic alternating direction method of multipliers for nonconvex optimization, in International Conference on Machine Learning, PMLR, Long Beach, CA, 2019, pp. 2839\u20132848.","DOI":"10.24963\/ijcai.2019\/354"},{"key":"CIT0017","unstructured":"F. Huang and S. Chen, Mini-batch stochastic admms for nonconvex nonsmooth optimization, preprint (2018), arXiv:1802.03284."},{"key":"CIT0018","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401399587"},{"key":"CIT0019","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-018-0034-y"},{"key":"CIT0020","unstructured":"R. Johnson and T. Zhang, Accelerating stochastic gradient descent using predictive variance reduction, in Advances in Neural Information Processing Systems, Curran Associates, Nevada, 2013, pp. 315\u2013323."},{"key":"CIT0021","unstructured":"Z. Li and J. Li, A simple proximal stochastic gradient method for nonsmooth nonconvex optimization, in Advances in Neural Information Processing Systems, Curran Associates, Montr\u00e9al, QC, 2018, pp. 5564\u20135574."},{"key":"CIT0022","unstructured":"B. Li, M. Ma, and G.B. Giannakis, On the convergence of SARAH and beyond, in International Conference on Artificial Intelligence and Statistics, PMLR, Palermo, 2020, pp. 223\u2013233."},{"key":"CIT0023","doi-asserted-by":"publisher","DOI":"10.1137\/140998135"},{"key":"CIT0024","doi-asserted-by":"publisher","DOI":"10.1137\/140971178"},{"key":"CIT0025","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-015-9282-8"},{"key":"CIT0026","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2020.3000512"},{"key":"CIT0027","doi-asserted-by":"publisher","DOI":"10.1137\/090753127"},{"key":"CIT0028","doi-asserted-by":"publisher","DOI":"10.1137\/110849468"},{"key":"CIT0029","unstructured":"L.M. Nguyen, J. Liu, K. Scheinberg, and M. Tak\u00e1\u010d, SARAH: A novel method for machine learning problems using stochastic recursive gradient, in International Conference on Machine Learning, PMLR, Sydney, 2017, pp. 2613\u20132621."},{"key":"CIT0030","first-page":"1","volume":"21","author":"Pham N.H.","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"CIT0031","unstructured":"S.J Reddi, S. Sra, B. Poczos, and A.J. Smola, Proximal stochastic methods for nonsmooth nonconvex finite-sum optimization, in Advances in Neural Information Processing Systems, Curran Associates, Barcelona, 2016, pp. 1145\u20131153."},{"key":"CIT0032","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729586"},{"key":"CIT0033","volume-title":"Variational Analysis","volume":"317","author":"Rockafellar R.T.","year":"2009"},{"key":"CIT0034","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-016-1030-6"},{"key":"CIT0035","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btg308"},{"key":"CIT0036","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008777829180"},{"key":"CIT0037","unstructured":"T. Suzuki, Dual averaging and proximal gradient descent for online alternating direction multiplier method, in International Conference on Machine Learning, PMLR, Atlanta, 2013, pp. 392\u2013400."},{"key":"CIT0038","unstructured":"T. Suzuki, Stochastic dual coordinate ascent with alternating direction method of multipliers, in International Conference on Machine Learning, PMLR, Beijing, 2014, pp. 736\u2013744."},{"key":"CIT0039","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"key":"CIT0040","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-017-9367-6","volume":"61","author":"Wang F.","year":"2018","journal-title":"Sci. China Info. Sci."},{"key":"CIT0041","unstructured":"Z. Wang, K. Ji, Y. Zhou, Y. Liang, and V. Tarokh, Spiderboost and momentum: Faster variance reduction algorithms, in Advances in Neural Information Processing Systems, Curran Associates, Vancouver, 2019, pp. 2406\u20132416."},{"key":"CIT0042","doi-asserted-by":"publisher","DOI":"10.1137\/140961791"},{"key":"CIT0043","unstructured":"S. Zheng and J.T. Kwok, Fast-and-light stochastic ADMM, in International Joint Conference on Artificial Intelligence, Morgan Kaufmann, New York, 2016, pp. 2407\u20132413."},{"key":"CIT0044","unstructured":"W. Zhong and J. Kwok, Fast stochastic alternating direction method of multipliers, in International Conference on Machine Learning, PMLR, Beijing, 2014, pp. 46\u201354."}],"container-title":["Optimization Methods and Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10556788.2022.2091562","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T14:42:21Z","timestamp":1677249741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10556788.2022.2091562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,19]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1,2]]}},"alternative-id":["10.1080\/10556788.2022.2091562"],"URL":"https:\/\/doi.org\/10.1080\/10556788.2022.2091562","relation":{},"ISSN":["1055-6788","1029-4937"],"issn-type":[{"value":"1055-6788","type":"print"},{"value":"1029-4937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,19]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=goms20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2021-05-12","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-05-30","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-07-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}