{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T21:06:09Z","timestamp":1768338369910,"version":"3.49.0"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2022,2,5]],"date-time":"2022-02-05T00:00:00Z","timestamp":1644019200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,5]],"date-time":"2022-02-05T00:00:00Z","timestamp":1644019200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["project 18-71-10108"],"award-info":[{"award-number":["project 18-71-10108"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"crossref","award":["075-00337-20-03"],"award-info":[{"award-number":["075-00337-20-03"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"crossref","award":["project no. 0714-2020-0005"],"award-info":[{"award-number":["project no. 0714-2020-0005"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s11590-021-01834-w","type":"journal-article","created":{"date-parts":[[2022,2,5]],"date-time":"2022-02-05T11:02:41Z","timestamp":1644058961000},"page":"2145-2175","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Stochastic saddle-point optimization for the Wasserstein barycenter problem"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8832-7926","authenticated-orcid":false,"given":"Daniil","family":"Tiapkin","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7386-039X","authenticated-orcid":false,"given":"Alexander","family":"Gasnikov","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1201-2343","authenticated-orcid":false,"given":"Pavel","family":"Dvurechensky","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,5]]},"reference":[{"issue":"2","key":"1834_CR1","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1137\/100805741","volume":"43","author":"M Agueh","year":"2011","unstructured":"Agueh, M., Carlier, G.: Barycenters in the wasserstein space. SIAM J. Math. Anal. 43(2), 904\u2013924 (2011)","journal-title":"SIAM J. Math. Anal."},{"issue":"8","key":"1834_CR2","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1134\/S0965542517080048","volume":"57","author":"AS Anikin","year":"2017","unstructured":"Anikin, A.S., Gasnikov, A.V., Dvurechensky, P.E., Tyurin, A.I., Chernov, A.V.: Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints. Comput. Math. Math. Phys. 57(8), 1262\u20131276 (2017)","journal-title":"Comput. Math. Math. Phys."},{"key":"1834_CR3","unstructured":"Antonakopoulos, K., Belmega, V., Mertikopoulos, P.: An adaptive mirror-prox method for variational inequalities with singular operators. In: Wallach, H., Larochelle, H., Beygelzimer, A., d\u2019Alch\u00e9-Buc, F., Fox, E., Garnett, R. (eds.) Advances in Neural Information Processing Systems 32, pp. 8455\u20138465. Curran Associates, Inc. http:\/\/papers.nips.cc\/paper\/9053-an-adaptive-mirror-prox-method-for-variational-inequalities-with-singular-operators.pdf (2019)"},{"key":"1834_CR4","unstructured":"Bach, F., Levy, K.Y.: A universal algorithm for variational inequalities adaptive to smoothness and noise. In: Beygelzimer, A., Hsu, D. (eds.) Proceedings of the Thirty-Second Conference on Learning Theory, Proceedings of Machine Learning Research, vol.\u00a099, pp. 164\u2013194. PMLR, Phoenix. http:\/\/proceedings.mlr.press\/v99\/bach19a.html. ArXiv:1902.01637 (2019)"},{"key":"1834_CR5","doi-asserted-by":"publisher","unstructured":"Bayandina, A., Dvurechensky, P., Gasnikov, A., Stonyakin, F., Titov, A.: Mirror descent and convex optimization problems with non-smooth inequality constraints. In: Giselsson, P., Rantzer, A. (eds.) Large-Scale and Distributed Optimization, chap.\u00a08, pp. 181\u2013215. Springer. https:\/\/doi.org\/10.1007\/978-3-319-97478-1_8. ArXiv:1710.06612 (2018)","DOI":"10.1007\/978-3-319-97478-1_8"},{"issue":"2","key":"1834_CR6","doi-asserted-by":"publisher","first-page":"A1111","DOI":"10.1137\/141000439","volume":"37","author":"JD Benamou","year":"2015","unstructured":"Benamou, J.D., Carlier, G., Cuturi, M., Nenna, L., Peyr\u00e9, G.: Iterative Bregman projections for regularized transportation problems. SIAM J. Sci. Comput. 37(2), A1111\u2013A1138 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"1834_CR7","unstructured":"Beznosikov, A., Dvurechensky, P., Koloskova, A., Samokhina, V., Stich, S.U., Gasnikov, A.: Decentralized local stochastic extra-gradient for variational inequalities. arXiv:2106.08315 (2021)"},{"key":"1834_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-38219-3","volume-title":"Real and Functional Analysis","author":"VI Bogachev","year":"2020","unstructured":"Bogachev, V.I., Smolyanov, O.G.: Real and Functional Analysis, vol. 4. Springer, Berlin (2020)"},{"key":"1834_CR9","doi-asserted-by":"publisher","unstructured":"Boissard, E., Le Gouic, T., Loubes, J.M.: Distribution\u2019s template estimate with wasserstein metrics. Bernoulli 21(2), 740\u2013759 (2015). https:\/\/doi.org\/10.3150\/13-BEJ585","DOI":"10.3150\/13-BEJ585"},{"key":"1834_CR10","doi-asserted-by":"publisher","unstructured":"Bubeck, S.: Convex optimization: Algorithms and complexity. Foundations and Trends\u00ae in Machine Learning 8(3-4), 231\u2013357 (2015). https:\/\/doi.org\/10.1561\/2200000050","DOI":"10.1561\/2200000050"},{"key":"1834_CR11","doi-asserted-by":"crossref","unstructured":"Chernov, A., Dvurechensky, P., Gasnikov, A.: Fast primal-dual gradient method for strongly convex minimization problems with linear constraints. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds.) Discrete Optimization and Operations Research: 9th International Conference, DOOR 2016, Vladivostok, Russia, September 19\u201323, 2016, Proceedings, pp. 391\u2013403. Springer (2016)","DOI":"10.1007\/978-3-319-44914-2_31"},{"key":"1834_CR12","unstructured":"Chewi, S., Maunu, T., Rigollet, P., Stromme, A.: Gradient descent algorithms for Bures-Wasserstein barycenters. In: Abernethy, J., Agarwal, S. (eds) Proceedings of Thirty Third Conference on Learning Theory, Proceedings of Machine Learning Research, vol. 125, pp. 1276\u20131304. PMLR. http:\/\/proceedings.mlr.press\/v125\/chewi20a.html (2020)"},{"key":"1834_CR13","unstructured":"Claici, S., Chien, E., Solomon, J.: Stochastic Wasserstein barycenters. In: Dy, J., Krause, A. (eds.) Proceedings of the 35th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol.\u00a080, pp. 999\u20131008. PMLR. http:\/\/proceedings.mlr.press\/v80\/claici18a.html (2018)"},{"key":"1834_CR14","unstructured":"Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transport. In: Burges, C.J.C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems 26, pp. 2292\u20132300. Curran Associates, Inc. (2013)"},{"key":"1834_CR15","unstructured":"Cuturi, M., Doucet, A.: Fast computation of wasserstein barycenters. In: Xing, E.P., Jebara, T. (eds.) Proceedings of the 31st International Conference on Machine Learning, Proceedings of Machine Learning Research, vol.\u00a032, pp. 685\u2013693. PMLR, Bejing, China. http:\/\/proceedings.mlr.press\/v32\/cuturi14.html (2014)"},{"issue":"2","key":"1834_CR16","doi-asserted-by":"publisher","first-page":"936","DOI":"10.1137\/19M1301047","volume":"13","author":"J Delon","year":"2020","unstructured":"Delon, J., Desolneux, A.: A wasserstein-type distance in the space of gaussian mixture models. SIAM J. Imaging Sci. 13(2), 936\u2013970 (2020). https:\/\/doi.org\/10.1137\/19M1301047","journal-title":"SIAM J. Imaging Sci."},{"key":"1834_CR17","doi-asserted-by":"crossref","unstructured":"Dvinskikh, D.: Stochastic averaging versus sample average approximation for population wasserstein barycenter calculation. arXiv:2001.07697 (2020)","DOI":"10.1080\/10556788.2021.1965600"},{"key":"1834_CR18","unstructured":"Dvinskikh, D.: Decentralized algorithms for wasserstein barycenters. arXiv:2105.01587 (2021)"},{"key":"1834_CR19","doi-asserted-by":"crossref","unstructured":"Dvinskikh, D., Gorbunov, E., Gasnikov, A., Dvurechensky, P., Uribe, C.A.: On primal and dual approaches for distributed stochastic convex optimization over networks. In: 2019 IEEE 58th Conference on Decision and Control (CDC), pp. 7435\u20137440. IEEE. ArXiv:1903.09844 (2019)","DOI":"10.1109\/CDC40024.2019.9029798"},{"key":"1834_CR20","unstructured":"Dvinskikh, D., Ogaltsov, A., Dvurechensky, P., Gasnikov, A., Spokoiny, V.: Adaptive gradient descent for convex and non-convex stochastic optimization. arXiv:1911.08380 (2019)"},{"key":"1834_CR21","doi-asserted-by":"publisher","unstructured":"Dvinskikh, D., Ogaltsov, A., Gasnikov, A., Dvurechensky, P., Spokoiny, V.: On the line-search gradient methods for stochastic optimization. IFAC-PapersOnLine 53(2), 1715\u20131720 (2020). https:\/\/doi.org\/10.1016\/j.ifacol.2020.12.2284. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S240589632032944X. 21th IFAC World Congress, arXiv:1911.08380","DOI":"10.1016\/j.ifacol.2020.12.2284"},{"key":"1834_CR22","unstructured":"Dvinskikh, D., Tiapkin, D.: Improved complexity bounds in wasserstein barycenter problem. In: Banerjee, A., Fukumizu, K. (eds.) Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, vol. 130, pp. 1738\u20131746. PMLR (2021). http:\/\/proceedings.mlr.press\/v130\/dvinskikh21a.html"},{"key":"1834_CR23","unstructured":"Dvurechensky, P., Dvinskikh, D., Gasnikov, A., Uribe, C.A., Nedi\u0107, A.: Decentralize and randomize: faster algorithm for Wasserstein barycenters. In: Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems 31, NeurIPS 2018, pp. 10783\u201310793. Curran Associates, Inc. http:\/\/papers.nips.cc\/paper\/8274-decentralize-and-randomize-faster-algorithm-for-wasserstein-barycenters.pdf. ArXiv:1806.03915 (2018)"},{"key":"1834_CR24","unstructured":"Dvurechensky, P., Gasnikov, A., Gasnikova, E., Matsievsky, S., Rodomanov, A., Usik, I.: Primal-dual method for searching equilibrium in hierarchical congestion population games. In: Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016) Vladivostok, Russia, September 19\u201323, 2016, pp. 584\u2013595. ArXiv:1606.08988 (2016)"},{"key":"1834_CR25","unstructured":"Dvurechensky, P., Gasnikov, A., Kroshnin, A.: Computational optimal transport: complexity by accelerated gradient descent is better than by Sinkhorn\u2019s algorithm. In: Dy, J., Krause, A. (eds.) Proceedings of the 35th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol.\u00a080, pp. 1367\u20131376. ArXiv:1802.04367 (2018)"},{"key":"1834_CR26","doi-asserted-by":"crossref","unstructured":"Dvurechensky, P., Gasnikov, A., Omelchenko, S., Tiurin, A.: A stable alternative to Sinkhorn\u2019s algorithm for regularized optimal transport. In: Kononov, A., Khachay, M., Kalyagin, V.A., Pardalos, P. (eds.) Mathematical Optimization Theory and Operations Research, pp. 406\u2013423. Springer, Cham (2020)","DOI":"10.1007\/978-3-030-49988-4_28"},{"key":"1834_CR27","doi-asserted-by":"crossref","unstructured":"Dvurechensky, P., Kamzolov, D., Lukashevich, A., Lee, S., Ordentlich, E., Uribe, C.A., Gasnikov, A.: Hyperfast second-order local solvers for efficient statistically preconditioned distributed optimization. arXiv:2102.08246 (2021)","DOI":"10.1016\/j.ejco.2022.100045"},{"key":"1834_CR28","unstructured":"Genevay, A., Cuturi, M., Peyr\u00e9, G., Bach, F.: Stochastic optimization for large-scale optimal transport. In: Advances in Neural Information Processing Systems, pp. 3440\u20133448 (2016)"},{"key":"1834_CR29","unstructured":"Gorbunov, E., Dvinskikh, D., Gasnikov, A.: Optimal Decentralized Distributed Algorithms for Stochastic Convex Optimization. arXiv:1911.07363 (2019)"},{"key":"1834_CR30","unstructured":"Gorbunov, E., Rogozin, A., Beznosikov, A., Dvinskikh, D., Gasnikov, A.: Recent theoretical advances in decentralized distributed convex optimization. arXiv preprint arXiv:2011.13259 (2020)"},{"key":"1834_CR31","unstructured":"Guminov, S., Dvurechensky, P., Tupitsa, N., Gasnikov, A.: On a combination of alternating minimization and Nesterov\u2019s momentum. In: M.\u00a0Meila, T.\u00a0Zhang (eds.) Proceedings of the 38th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 139, pp. 3886\u20133898. PMLR, Virtual (2021). http:\/\/proceedings.mlr.press\/v139\/guminov21a.html. ArXiv:1906.03622, WIAS Preprint No. 2695"},{"issue":"2","key":"1834_CR32","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1134\/S1064562419020042","volume":"99","author":"SV Guminov","year":"2019","unstructured":"Guminov, S.V., Nesterov, Y.E., Dvurechensky, P.E., Gasnikov, A.V.: Accelerated primal-dual gradient descent with linesearch for convex, nonconvex, and nonsmooth optimization problems. Dokl. Math. 99(2), 125\u2013128 (2019)","journal-title":"Dokl. Math."},{"key":"1834_CR33","unstructured":"Heinemann, F., Munk, A., Zemel, Y.: Randomised wasserstein barycenter computation: Resampling with statistical guarantees. arXiv:2012.06397 (2020)"},{"key":"1834_CR34","unstructured":"Hendrikx, H., Bach, F., Massoulie, L.: An optimal algorithm for decentralized finite sum optimization. arXiv:2005.10675 (2020)"},{"key":"1834_CR35","unstructured":"Hendrikx, H., Xiao, L., Bubeck, S., Bach, F., Massoulie, L.: Statistically preconditioned accelerated gradient method for distributed optimization. In: III, H.D., Singh, A. (eds.) Proceedings of the 37th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 119, pp. 4203\u20134227. PMLR. http:\/\/proceedings.mlr.press\/v119\/hendrikx20a.html (2020)"},{"key":"1834_CR36","doi-asserted-by":"publisher","unstructured":"Krawtschenko, R., Uribe, C.A., Gasnikov, A., Dvurechensky, P.: Distributed optimization with quantization for computing wasserstein barycenters. arXiv:2010.14325, https:\/\/doi.org\/10.20347\/WIAS.PREPRINT.2782. WIAS preprint 2782 (2020)","DOI":"10.20347\/WIAS.PREPRINT.2782"},{"issue":"3","key":"1834_CR37","doi-asserted-by":"publisher","first-page":"1264","DOI":"10.1214\/20-AAP1618","volume":"31","author":"A Kroshnin","year":"2021","unstructured":"Kroshnin, A., Spokoiny, V., Suvorikova, A.: Statistical inference for Bures-Wasserstein barycenters. Ann. Appl. Probab. 31(3), 1264\u20131298 (2021). https:\/\/doi.org\/10.1214\/20-AAP1618","journal-title":"Ann. Appl. Probab."},{"key":"1834_CR38","unstructured":"Kroshnin, A., Tupitsa, N., Dvinskikh, D., Dvurechensky, P., Gasnikov, A., Uribe, C.: On the complexity of approximating Wasserstein barycenters. In: Chaudhuri, K., Salakhutdinov, R. (eds.) Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol.\u00a097, pp. 3530\u20133540. PMLR, Long Beach, California, USA. ArXiv:1901.08686 (2019)"},{"key":"1834_CR39","first-page":"129","volume":"6","author":"J Lafferty","year":"2005","unstructured":"Lafferty, J., Lebanon, G.: Diffusion kernels on statistical manifolds. J. Mach. Learn. Res. 6, 129\u2013163 (2005)","journal-title":"J. Mach. Learn. Res."},{"key":"1834_CR40","unstructured":"Lin, T., Ho, N., Chen, X., Cuturi, M., Jordan, M.I.: Revisiting fixed support wasserstein barycenter: computational hardness and efficient algorithms. arXiv:2002.04783 (2020)"},{"key":"1834_CR41","unstructured":"Lin, T., Ho, N., Jordan, M.: On efficient optimal transport: An analysis of greedy and accelerated mirror descent algorithms. In: Chaudhuri, K., Salakhutdinov, R. (eds.) Proceedings of the 36th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol.\u00a097, pp. 3982\u20133991. PMLR, Long Beach, California, USA (2019)"},{"key":"1834_CR42","unstructured":"Mensch, A., Peyr\u00e9, G.: Online sinkhorn: optimal transport distances from sample streams. In: Advances in Neural Information Processing Systems, vol. 33 (2020)"},{"key":"1834_CR43","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s00365-009-9080-0","volume":"44","author":"HQ Minh","year":"2010","unstructured":"Minh, H.Q.: Nonparametric stochastic approximation with large step-sizes. Some Properties of Gaussian Reproducing Kernel Hilbert Spaces and Their Implications for Function Approximation and Learning Theory 44, 307\u2013338 (2010). https:\/\/doi.org\/10.1007\/s00365-009-9080-0","journal-title":"Some Properties of Gaussian Reproducing Kernel Hilbert Spaces and Their Implications for Function Approximation and Learning Theory"},{"key":"1834_CR44","volume-title":"Foundations of Machine Learning","author":"M Mohri","year":"2018","unstructured":"Mohri, M., Rostamizadeh, A., Talwalkar, A.: Foundations of Machine Learning. MIT Press, London (2018)"},{"issue":"4","key":"1834_CR45","doi-asserted-by":"publisher","first-page":"1574","DOI":"10.1137\/070704277","volume":"19","author":"A Nemirovski","year":"2009","unstructured":"Nemirovski, A., Juditsky, A., Lan, G., Shapiro, A.: Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4), 1574\u20131609 (2009). https:\/\/doi.org\/10.1137\/070704277","journal-title":"SIAM J. Optim."},{"key":"1834_CR46","volume-title":"Problem Complexity and Method Efficiency in Optimization","author":"A Nemirovsky","year":"1983","unstructured":"Nemirovsky, A., Yudin, D.: Problem Complexity and Method Efficiency in Optimization. Wiley, New York (1983)"},{"key":"1834_CR47","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2020.1731747","author":"Y Nesterov","year":"2020","unstructured":"Nesterov, Y., Gasnikov, A., Guminov, S., Dvurechensky, P.: Primal-dual accelerated gradient methods with small-dimensional relaxation oracle. Optim. Methods Softw. (2020). https:\/\/doi.org\/10.1080\/10556788.2020.1731747","journal-title":"Optim. Methods Softw."},{"issue":"5\u20136","key":"1834_CR48","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/2200000073","volume":"11","author":"G Peyr\u00e9","year":"2019","unstructured":"Peyr\u00e9, G., Cuturi, M.: Computational optimal transport. Found. Trends Mach. Learn. 11(5\u20136), 355\u2013607 (2019)","journal-title":"Found. Trends Mach. Learn."},{"key":"1834_CR49","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"2009","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis, vol. 317. Springer, Berlin (2009)"},{"key":"1834_CR50","unstructured":"Rogozin, A., Beznosikov, A., Dvinskikh, D., Kovalev, D., Dvurechensky, P., Gasnikov, A.: Decentralized distributed optimization for saddle point problems. arXiv:2102.07758 (2021)"},{"key":"1834_CR51","doi-asserted-by":"crossref","unstructured":"Rogozin, A., Bochko, M., Dvurechensky, P., Gasnikov, A., Lukoshkin, V.: An accelerated method for decentralized distributed stochastic optimization over time-varying graphs. arXiv:2103.15598 (2021)","DOI":"10.1109\/CDC45484.2021.9683110"},{"key":"1834_CR52","unstructured":"Scaman, K., Bach, F., Bubeck, S., Lee, Y.T., Massouli\u00e9, L.: Optimal algorithms for smooth and strongly convex distributed optimization in networks. In: Precup, D., Teh, Y.W. (eds.) Proceedings of the 34th International Conference on Machine Learning, Proceedings of Machine Learning Research, vol.\u00a070, pp. 3027\u20133036. PMLR, International Convention Centre, Sydney. http:\/\/proceedings.mlr.press\/v70\/scaman17a.html (2017)"},{"issue":"3","key":"1834_CR53","doi-asserted-by":"publisher","first-page":"A1443","DOI":"10.1137\/16M1106018","volume":"41","author":"B Schmitzer","year":"2019","unstructured":"Schmitzer, B.: Stabilized sparse scaling algorithms for entropy regularized transport problems. SIAM J. Sci. Comput. 41(3), A1443\u2013A1481 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"1834_CR54","unstructured":"Staib, M., Claici, S., Solomon, J.M., Jegelka, S.: Parallel streaming wasserstein barycenters. In: Guyon, I., Luxburg, U.V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., Garnett, R. (eds.) Advances in Neural Information Processing Systems 30, pp. 2647\u20132658. Curran Associates, Inc. http:\/\/papers.nips.cc\/paper\/6858-parallel-streaming-wasserstein-barycenters.pdf (2017)"},{"key":"1834_CR55","volume-title":"Support Vector Machines","author":"I Steinwart","year":"2008","unstructured":"Steinwart, I., Christmann, A.: Support Vector Machines. Springer, Berlin (2008)"},{"key":"1834_CR56","unstructured":"Stonyakin, F., Gasnikov, A., Dvurechensky, P., Alkousa, M., Titov, A.: Generalized Mirror Prox for monotone variational inequalities: universality and inexact oracle. arXiv:1806.05140 (2018)"},{"key":"1834_CR57","doi-asserted-by":"publisher","unstructured":"Stonyakin, F., Tyurin, A., Gasnikov, A., Dvurechensky, P., Agafonov, A., Dvinskikh, D., Alkousa, M., Pasechnyuk, D., Artamonov, S., Piskunova, V.: Inexact model: A framework for optimization and variational inequalities. Optimization Methods and Software. https:\/\/doi.org\/10.1080\/10556788.2021.1924714. WIAS Preprint No. 2709, arXiv:2001.09013, arXiv:1902.00990 (2021)","DOI":"10.1080\/10556788.2021.1924714"},{"key":"1834_CR58","doi-asserted-by":"crossref","unstructured":"Stonyakin, F.S., Dvinskikh, D., Dvurechensky, P., Kroshnin, A., Kuznetsova, O., Agafonov, A., Gasnikov, A., Tyurin, A., Uribe, C.A., Pasechnyuk, D., Artamonov, S.: Gradient methods for problems with inexact model of the objective. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds.) Mathematical Optimization Theory and Operations Research, pp. 97\u2013114. Springer, Cham (2019). ArXiv:1902.09001","DOI":"10.1007\/978-3-030-22629-9_8"},{"key":"1834_CR59","doi-asserted-by":"crossref","unstructured":"Uribe, C.A., Dvinskikh, D., Dvurechensky, P., Gasnikov, A., Nedi\u0107, A.: Distributed computation of Wasserstein barycenters over networks. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 6544\u20136549. ArXiv:1803.02933 (2018)","DOI":"10.1109\/CDC.2018.8619160"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-021-01834-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-021-01834-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-021-01834-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,26]],"date-time":"2023-01-26T00:50:50Z","timestamp":1674694250000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-021-01834-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,5]]},"references-count":59,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["1834"],"URL":"https:\/\/doi.org\/10.1007\/s11590-021-01834-w","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,5]]},"assertion":[{"value":"10 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The Gaussian measures dataset generated during the current study is available from the corresponding author on reasonable request. The dataset MNIST is available on the website.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Availability of data and materials"}},{"value":"The code used during the current study is available from the corresponding author on reasonable request.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}]}}