{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T05:16:39Z","timestamp":1768281399309,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100020409","name":"Analytical Center for the Government of the Russian Federation","doi-asserted-by":"publisher","award":["000000D730321P5Q0002"],"award-info":[{"award-number":["000000D730321P5Q0002"]}],"id":[{"id":"10.13039\/100020409","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10287-023-00485-9","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T08:01:53Z","timestamp":1699257713000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Decentralized saddle-point problems with different constants of strong convexity and strong concavity"],"prefix":"10.1007","volume":"21","author":[{"given":"Dmitry","family":"Metelev","sequence":"first","affiliation":[]},{"given":"Alexander","family":"Rogozin","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Gasnikov","sequence":"additional","affiliation":[]},{"given":"Dmitry","family":"Kovalev","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"issue":"11","key":"485_CR1","doi-asserted-by":"publisher","first-page":"1787","DOI":"10.1134\/S0965542520110020","volume":"60","author":"MS Alkousa","year":"2020","unstructured":"Alkousa MS, Gasnikov AV, Dvinskikh DM, Kovalev DA, Stonyakin FS (2020) Accelerated methods for saddle-point problem. Computat Math Math Phys 60(11):1787\u20131809","journal-title":"Computat Math Math Phys"},{"key":"485_CR2","unstructured":"Beznosikov A, Gorbunov E, Berard H, Loizou N (2022) Stochastic gradient descent-ascent: unified theory and new efficient methods. arXiv preprint arXiv:2202.07262"},{"key":"485_CR3","doi-asserted-by":"crossref","unstructured":"Beznosikov A, Rogozin A, Kovalev D, Gasnikov A (2021) Near-optimal decentralized algorithms for saddle point problems over time-varying networks. In: International conference on optimization and applications. Springer, pp 246\u2013257","DOI":"10.1007\/978-3-030-91059-4_18"},{"key":"485_CR4","unstructured":"Beznosikov A, Samokhin V, Gasnikov A (2020) Distributed saddle-point problems: lower bounds, optimal and robust algorithms. arXiv preprint arXiv:2010.13112"},{"issue":"1","key":"485_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2011","unstructured":"Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1\u2013122","journal-title":"Found Trends Mach Learn"},{"issue":"1","key":"485_CR6","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10107-013-0677-5","volume":"146","author":"O Devolder","year":"2014","unstructured":"Devolder O, Glineur F, Nesterov Y (2014) First-order methods of smooth convex optimization with inexact oracle. Math Program 146(1):37\u201375","journal-title":"Math Program"},{"key":"485_CR7","unstructured":"Du SS, Gidel G, Jordan MI, Li CJ (2022) Optimal extragradient-based bilinearly-coupled saddle-point optimization. arXiv preprint arXiv:2206.08573"},{"key":"485_CR8","unstructured":"Gasnikov A, Novitskii A, Novitskii V, Abdukhakimov F, Kamzolov D, Beznosikov A, Tak\u00e1\u010d M, Dvurechensky P, Gu B (2022) The power of first-order smooth optimization for black-box non-smooth problems. arXiv preprint arXiv:2201.12289"},{"key":"485_CR9","unstructured":"Gorbunov E, Berard H, Gidel G, Loizou N (2021) Stochastic extragradient: general analysis and improved rates. arXiv preprint arXiv:2111.08611"},{"key":"485_CR10","unstructured":"Gorbunov E, Rogozin A, Beznosikov A, Dvinskikh D, Gasnikov A (2020) Recent theoretical advances in decentralized distributed convex optimization. arXiv preprint arXiv:2011.13259"},{"key":"485_CR11","unstructured":"Ibrahim A, Azizian W, Gidel G, Mitliagkas I (2020) Linear lower bounds and conditioning of differentiable games. In: International conference on machine learning. PMLR, pp 4583\u20134593"},{"key":"485_CR12","unstructured":"Jin Y, Sidford A, Tian K (2022) Sharper rates for separable minimax and finite sum optimization via primal\u2013dual extragradient methods. arXiv preprint arXiv:2202.04640"},{"key":"485_CR13","first-page":"18342","volume":"33","author":"D Kovalev","year":"2020","unstructured":"Kovalev D, Salim A, Richt\u00e1rik P (2020) Optimal and practical algorithms for smooth and strongly convex decentralized optimization. Adv Neural Inf Process Syst 33:18342\u201318352","journal-title":"Adv Neural Inf Process Syst"},{"key":"485_CR14","first-page":"22325","volume":"34","author":"D Kovalev","year":"2021","unstructured":"Kovalev D, Gasanov E, Gasnikov A, Richtarik P (2021) Lower bounds and optimal algorithms for smooth and strongly convex decentralized optimization over time-varying networks. Adv Neural Inf Process Syst 34:22325\u201322335","journal-title":"Adv Neural Inf Process Syst"},{"key":"485_CR15","unstructured":"Kovalev D, Beznosikov A, Sadiev A, Persiianov M, Richt\u00e1rik P, Gasnikov A (2022) Optimal algorithms for decentralized stochastic variational inequalities. arXiv preprint arXiv:2202.02771"},{"key":"485_CR16","unstructured":"Kovalev D, Gasnikov A (2022) The first optimal algorithm for smooth and strongly-convex-strongly-concave minimax optimization. arXiv preprint arXiv:2205.05653"},{"key":"485_CR17","unstructured":"Kovalev D, Gasnikov A, Richt\u00e1rik P (2021) Accelerated primal-dual gradient method for smooth and convex\u2013concave saddle-point problems with bilinear coupling. arXiv preprint arXiv:2112.15199"},{"key":"485_CR18","unstructured":"Kovalev D, Shulgin E, Richt\u00e1rik P, Rogozin AV, Gasnikov A (2021) Adom: accelerated decentralized optimization method for time-varying networks. In: International conference on machine learning. PMLR, pp 5784\u20135793"},{"key":"485_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-39568-1","volume-title":"First-order and stochastic optimization methods for machine learning","author":"G Lan","year":"2020","unstructured":"Lan G (2020) First-order and stochastic optimization methods for machine learning. Springer, New York"},{"key":"485_CR20","unstructured":"Li H, Lin Z (2021) Accelerated gradient tracking over time-varying graphs for decentralized optimization. arXiv preprint arXiv:2104.02596"},{"key":"485_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-15-2910-8","volume-title":"Accelerated optimization for machine learning","author":"Z Lin","year":"2020","unstructured":"Lin Z, Li H, Fang C (2020) Accelerated optimization for machine learning. Springer, New York"},{"key":"485_CR22","unstructured":"Lin T, Jin C, Jordan MI (2020) Near-optimal algorithms for minimax optimization. In: Conference on learning theory. PMLR, pp 2738\u20132779"},{"key":"485_CR23","unstructured":"Luo L, Ye H (2022) Decentralized stochastic variance reduced extragradient method"},{"key":"485_CR24","volume-title":"Problem complexity and method efficiency in optimization","author":"A Nemirovski","year":"1983","unstructured":"Nemirovski A, Yudin D (1983) Problem complexity and method efficiency in optimization. Wiley, New York"},{"key":"485_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-91578-4","volume-title":"Lectures on convex optimization","author":"Y Nesterov","year":"2018","unstructured":"Nesterov Y (2018) Lectures on convex optimization, vol 137. Springer, New York"},{"key":"485_CR26","unstructured":"Rogozin A, Beznosikov A, Dvinskikh D, Kovalev D, Dvurechensky P, Gasnikov A (2021) Decentralized distributed optimization for saddle point problems. arXiv preprint arXiv:2102.07758"},{"key":"485_CR27","doi-asserted-by":"crossref","unstructured":"Rogozin A, Bochko M, Dvurechensky P, Gasnikov A, Lukoshkin, V (2021) An accelerated method for decentralized distributed stochastic optimization over time-varying graphs. arXiv preprint arXiv:2103.15598","DOI":"10.1109\/CDC45484.2021.9683110"},{"key":"485_CR28","doi-asserted-by":"crossref","unstructured":"Rogozin A, Lukoshkin V, Gasnikov A, Kovalev D, Shulgin E (2021) Towards accelerated rates for distributed optimization over time-varying networks. In: International conference on optimization and applications. Springer, pp 258\u2013272","DOI":"10.1007\/978-3-030-91059-4_19"},{"key":"485_CR29","unstructured":"Scaman K, Bach F, Bubeck S, Lee YT, Massouli\u00e9 L (2017) Optimal algorithms for smooth and strongly convex distributed optimization in networks"},{"key":"485_CR30","doi-asserted-by":"crossref","unstructured":"Song Z, Shi L, Pu S, Yan M (2021) Optimal gradient tracking for decentralized optimization. arXiv preprint arXiv:2110.05282","DOI":"10.1109\/TSP.2022.3160238"},{"key":"485_CR31","unstructured":"Thekumparampil KK, He N, Oh S (2022) Lifted primal\u2013dual method for bilinearly coupled smooth minimax optimization. arXiv preprint arXiv:2201.07427"},{"key":"485_CR32","unstructured":"Tian Y, Scutari G, Cao T, Gasnikov A (2021) Acceleration in distributed optimization under similarity. arXiv preprint arXiv:2110.12347"},{"key":"485_CR33","unstructured":"Tominin V, Tominin Y, Borodich E, Kovalev D, Gasnikov A, Dvurechensky P (2021) On accelerated methods for saddle-point problems with composite structure. arXiv preprint arXiv:2103.09344"},{"issue":"2","key":"485_CR34","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1137\/S0363012998338806","volume":"38","author":"P Tseng","year":"2000","unstructured":"Tseng P (2000) A modified forward\u2013backward splitting method for maximal monotone mappings. SIAM J Control Optim 38(2):431\u2013446","journal-title":"SIAM J Control Optim"},{"key":"485_CR35","first-page":"4800","volume":"33","author":"Y Wang","year":"2020","unstructured":"Wang Y, Li J (2020) Improved algorithms for convex\u2013concave minimax optimization. Adv Neural Inf Process Syst 33:4800\u20134810","journal-title":"Adv Neural Inf Process Syst"},{"key":"485_CR36","doi-asserted-by":"crossref","unstructured":"Yarmoshik D, Rogozin A, Khamisov O, Dvurechensky P, Gasnikov A et al (2022) Decentralized convex optimization under affine constraints for power systems control. arXiv preprint arXiv:2203.16686","DOI":"10.1007\/978-3-031-09607-5_5"},{"key":"485_CR37","unstructured":"Zhang X, Aybat NS, Gurbuzbalaban M (2021) Robust accelerated primal-dual methods for computing saddle points. arXiv preprint arXiv:2111.12743"},{"key":"485_CR38","unstructured":"Zhang J, Hong M, Zhang S (2019) On lower iteration complexity bounds for the saddle point problems. arXiv preprint arXiv:1912.07481"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-023-00485-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10287-023-00485-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-023-00485-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T12:08:20Z","timestamp":1719058100000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10287-023-00485-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,6]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["485"],"URL":"https:\/\/doi.org\/10.1007\/s10287-023-00485-9","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,6]]},"assertion":[{"value":"30 June 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 October 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"5"}}