{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:24:29Z","timestamp":1740122669392,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T00:00:00Z","timestamp":1649721600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T00:00:00Z","timestamp":1649721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100008982","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1319050","1637473","1637474"],"award-info":[{"award-number":["1319050","1637473","1637474"]}],"id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N00014-16-1-2802"],"award-info":[{"award-number":["N00014-16-1-2802"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100006831","name":"U.S. Air Force","doi-asserted-by":"publisher","award":["FA9453-19-1-0078"],"award-info":[{"award-number":["FA9453-19-1-0078"]}],"id":[{"id":"10.13039\/100006831","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N00014-19-1-2295"],"award-info":[{"award-number":["N00014-19-1-2295"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s10589-022-00365-z","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T17:15:49Z","timestamp":1649783749000},"page":"361-394","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Accelerated gradient sliding for structured convex optimization"],"prefix":"10.1007","volume":"82","author":[{"given":"Guanghui","family":"Lan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2609-4805","authenticated-orcid":false,"given":"Yuyuan","family":"Ouyang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,12]]},"reference":[{"key":"365_CR1","unstructured":"Arrow, K., Hurwicz, L., Uzawa, H.: Studies in Linear and Non-linear Programming. Stanford Mathematical Studies in the Social Sciences. Stanford University Press (1958). http:\/\/books.google.com\/books?id=jWi4AAAAIAAJ"},{"issue":"3","key":"365_CR2","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1137\/S1052623403427823","volume":"16","author":"A Auslender","year":"2006","unstructured":"Auslender, A., Teboulle, M.: Interior gradient and proximal methods for convex and conic optimization. SIAM J. Optim. 16(3), 697\u2013725 (2006)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"365_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/090756855","volume":"4","author":"S Becker","year":"2011","unstructured":"Becker, S., Bobin, J., Cand\u00e8s, E.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 4(1), 1\u201339 (2011)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"365_CR4","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/0041-5553(67)90040-7","volume":"7","author":"LM Bregman","year":"1967","unstructured":"Bregman, L.M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7(3), 200\u2013217 (1967)","journal-title":"USSR Comput. Math. Math. Phys."},{"issue":"1","key":"365_CR5","first-page":"89","volume":"20","author":"A Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20(1), 89\u201397 (2004)","journal-title":"J. Math. Imaging Vis."},{"issue":"1","key":"365_CR6","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A Chambolle","year":"2011","unstructured":"Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"365_CR7","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1017\/S096249291600009X","volume":"25","author":"A Chambolle","year":"2016","unstructured":"Chambolle, A., Pock, T.: An introduction to continuous optimization for imaging. Acta Numerica 25, 161\u2013319 (2016)","journal-title":"Acta Numerica"},{"issue":"1","key":"365_CR8","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s10107-015-0957-3","volume":"159","author":"A Chambolle","year":"2016","unstructured":"Chambolle, A., Pock, T.: On the ergodic convergence rates of a first-order primal-dual algorithm. Math. Program. 159(1), 253\u2013287 (2016)","journal-title":"Math. Program."},{"key":"365_CR9","unstructured":"Chen, Y., Lan, G., Ouyang, Y.: Accelerated schemes for a class of variational inequalities. arXiv preprint arXiv:1403.4164 (2014)"},{"issue":"4","key":"365_CR10","doi-asserted-by":"publisher","first-page":"1779","DOI":"10.1137\/130919362","volume":"24","author":"Y Chen","year":"2014","unstructured":"Chen, Y., Lan, G., Ouyang, Y.: Optimal primal-dual methods for a class of saddle point problems. SIAM J. Optim. 24(4), 1779\u20131814 (2014)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"365_CR11","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1137\/060676386","volume":"19","author":"A d\u2019Aspremont","year":"2008","unstructured":"d\u2019Aspremont, A.: Smooth optimization with approximate gradient. SIAM J. Optim. 19(3), 1171\u20131183 (2008)","journal-title":"SIAM J. Optim."},{"issue":"1\u20133","key":"365_CR12","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55(1\u20133), 293\u2013318 (1992)","journal-title":"Math. Program."},{"issue":"4","key":"365_CR13","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1137\/09076934X","volume":"3","author":"E Esser","year":"2010","unstructured":"Esser, E., Zhang, X., Chan, T.: A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. SIAM J. Imaging Sci. 3(4), 1015\u20131046 (2010)","journal-title":"SIAM J. Imaging Sci."},{"issue":"4","key":"365_CR14","doi-asserted-by":"publisher","first-page":"1469","DOI":"10.1137\/110848864","volume":"22","author":"S Ghadimi","year":"2012","unstructured":"Ghadimi, S., Lan, G.: Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization i: a generic algorithmic framework. SIAM J. Optim. 22(4), 1469\u20131492 (2012)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"365_CR15","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1137\/100814494","volume":"5","author":"B He","year":"2012","unstructured":"He, B., Yuan, X.: Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective. SIAM J. Imaging Sci. 5(1), 119\u2013149 (2012)","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"365_CR16","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1137\/110836936","volume":"50","author":"B He","year":"2012","unstructured":"He, B., Yuan, X.: On the O(1\/n) convergence rate of the Douglas-Rdachford alternating direction method. SIAM J. Numer. Anal. 50(2), 700\u2013709 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"365_CR17","unstructured":"He, N., Juditsky, A., Nemirovski, A.: Mirror prox algorithm for multi-term composite minimization and alternating directions. arXiv preprint arXiv:1311.1098 (2013)"},{"key":"365_CR18","unstructured":"He, Y., Monteiro, R.D.: Accelerating block-decomposition first-order methods for solving generalized saddle-point and nash equilibrium problems. Optimization-online preprint (2013)"},{"key":"365_CR19","unstructured":"He, Y., Monteiro, R.D.: An accelerated hpe-type algorithm for a class of composite convex-concave saddle-point problems. Submitt. SIAM J. Optim. (2014)"},{"issue":"2","key":"365_CR20","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1287\/moor.1100.0452","volume":"35","author":"S Hoda","year":"2010","unstructured":"Hoda, S., Gilpin, A., Pena, J., Sandholm, T.: Smoothing techniques for computing nash equilibria of sequential games. Math. Oper. Res. 35(2), 494\u2013512 (2010)","journal-title":"Math. Oper. Res."},{"key":"365_CR21","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1287\/10-SSY011","volume":"1","author":"A Juditsky","year":"2011","unstructured":"Juditsky, A., Nemirovski, A., Tauvel, C.: Solving variational inequalities with stochastic mirror-prox algorithm. Stoch. Syst. 1, 17\u201358 (2011)","journal-title":"Stoch. Syst."},{"issue":"1","key":"365_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-013-0737-x","volume":"149","author":"G Lan","year":"2015","unstructured":"Lan, G.: Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization. Math. Program. 149(1), 1\u201345 (2015)","journal-title":"Math. Program."},{"issue":"1\u20132","key":"365_CR23","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s10107-015-0955-5","volume":"159","author":"G Lan","year":"2016","unstructured":"Lan, G.: Gradient sliding for composite optimization. Math. Program. 159(1\u20132), 201\u2013235 (2016)","journal-title":"Math. Program."},{"issue":"1","key":"365_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-008-0261-6","volume":"126","author":"G Lan","year":"2011","unstructured":"Lan, G., Lu, Z., Monteiro, R.D.: Primal-dual first-order methods with $$\\cal{O}(1\/\\epsilon )$$ iteration-complexity for cone programming. Math. Program. 126(1), 1\u201329 (2011)","journal-title":"Math. Program."},{"issue":"2","key":"365_CR25","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s10851-014-0523-2","volume":"51","author":"DA Lorenz","year":"2015","unstructured":"Lorenz, D.A., Pock, T.: An inertial forward-backward algorithm for monotone inclusions. J. Math. Imaging Vis. 51(2), 311\u2013325 (2015)","journal-title":"J. Math. Imaging Vis."},{"issue":"1","key":"365_CR26","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1137\/110849468","volume":"23","author":"RD Monteiro","year":"2013","unstructured":"Monteiro, R.D., Svaiter, B.F.: Iteration-complexity of block-decomposition algorithms and the alternating direction method of multipliers. SIAM J. Optim. 23(1), 475\u2013507 (2013)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"365_CR27","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1137\/S1052623403425629","volume":"15","author":"A Nemirovski","year":"2004","unstructured":"Nemirovski, A.: Prox-method with rate of convergence $${O}(1\/t)$$ for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1), 229\u2013251 (2004)","journal-title":"SIAM J. Optim."},{"key":"365_CR28","series-title":"Wiley-Interscience Series in Discrete Mathematics","volume-title":"Problem Complexity and Method Efficiency in Optimization","author":"A Nemirovski","year":"1983","unstructured":"Nemirovski, A., Yudin, D.: Problem Complexity and Method Efficiency in Optimization. Wiley-Interscience Series in Discrete Mathematics, Wiley, New York (1983)"},{"issue":"1","key":"365_CR29","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1137\/S1052623403422285","volume":"16","author":"Y Nesterov","year":"2005","unstructured":"Nesterov, Y.: Excessive gap technique in nonsmooth convex minimization. SIAM J. Optim. 16(1), 235\u2013249 (2005)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"365_CR30","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Y Nesterov","year":"2005","unstructured":"Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. 103(1), 127\u2013152 (2005)","journal-title":"Math. Program."},{"key":"365_CR31","first-page":"543","volume":"269","author":"YE Nesterov","year":"1983","unstructured":"Nesterov, Y.E.: A method for unconstrained convex minimization problem with the rate of convergence $$O(1\/k^2)$$. Doklady AN SSSR 269, 543\u2013547 (1983)","journal-title":"Doklady AN SSSR"},{"key":"365_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course","author":"YE Nesterov","year":"2004","unstructured":"Nesterov, Y.E.: Introductory Lectures on Convex Optimization: A Basic Course. Kluwer Academic Publishers, Norwell (2004)"},{"key":"365_CR33","unstructured":"Ouyang, H., He, N., Tran, L., Gray, A.G.: Stochastic alternating direction method of multipliers. In: Proceedings of the 30th International Conference on Machine Learning (ICML-13), pp. 80\u201388 (2013)"},{"issue":"1","key":"365_CR34","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1137\/14095697X","volume":"8","author":"Y Ouyang","year":"2015","unstructured":"Ouyang, Y., Chen, Y., Lan, G., Eduardo Pasiliao, J.: An accelerated linearized alternating direction method of multipliers. SIAM J. Imaging Sci. 8(1), 644\u2013681 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"365_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-019-01420-0","volume":"185","author":"Y Ouyang","year":"2021","unstructured":"Ouyang, Y., Xu, Y.: Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems. Math. Program. 185(1), 1\u201335 (2021)","journal-title":"Math. Program."},{"key":"365_CR36","unstructured":"Tseng, P.: On accelerated proximal gradient methods for convex-concave optimization. Submitt. SIAM J. Optim. (2008)"},{"key":"365_CR37","unstructured":"Zhu, M., Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. UCLA CAM Report, pp. 08\u201334 (2008)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-022-00365-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-022-00365-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-022-00365-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T12:19:12Z","timestamp":1652962752000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-022-00365-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,12]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["365"],"URL":"https:\/\/doi.org\/10.1007\/s10589-022-00365-z","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2022,4,12]]},"assertion":[{"value":"13 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}