{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:19:26Z","timestamp":1774628366565,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2015,7,2]],"date-time":"2015-07-02T00:00:00Z","timestamp":1435795200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s11590-015-0916-1","type":"journal-article","created":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T10:59:18Z","timestamp":1435748358000},"page":"1233-1243","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["On optimal probabilities in stochastic coordinate descent methods"],"prefix":"10.1007","volume":"10","author":[{"given":"Peter","family":"Richt\u00e1rik","sequence":"first","affiliation":[]},{"given":"Martin","family":"Tak\u00e1\u010d","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,7,2]]},"reference":[{"key":"916_CR1","doi-asserted-by":"crossref","unstructured":"Bian, Y., Li, X., Liu, Y.: Parallel coordinate descent Newton for large-scale l1-regularized minimization. arXiv:1306.4080v1 (2013)","DOI":"10.1109\/TNNLS.2018.2889976"},{"key":"916_CR2","unstructured":"Bradley, J., Kyrola, A., Bickson, D., Guestrin, C.: Parallel coordinate descent for L1-regularized loss minimization. In: International Conference on Machine Learning (2011)"},{"key":"916_CR3","unstructured":"Csiba, D., Richt\u00e1rik, P.: Primal method for ERM with flexible mini-batching schemes and non-convex losses. arXiv:1506.02227 (2015)"},{"key":"916_CR4","unstructured":"Dang, C.D., Lan, G.: Stochastic block mirror descent methods for nonsmooth and stochastic optimization. In: Technical report, Georgia Institute of Technology (2013)"},{"key":"916_CR5","doi-asserted-by":"crossref","unstructured":"Fercoq, O.: Parallel coordinate descent for the AdaBoost problem. In: ICMLA, vol. 1, pp. 354\u2013358. IEEE, 2013","DOI":"10.1109\/ICMLA.2013.72"},{"key":"916_CR6","unstructured":"Fercoq, O., Richt\u00e1rik, P.: Smooth minimization of nonsmooth functions with parallel coordinate descent methods. arXiv:1309.5885 (2013)"},{"key":"916_CR7","doi-asserted-by":"crossref","unstructured":"Gower, R., Richt\u00e1rik, P.: Randomized iterative methods for linear systems. In: Technical report, University of Edinburgh (2015)","DOI":"10.1137\/15M1025487"},{"key":"916_CR8","doi-asserted-by":"crossref","unstructured":"Hsieh, C.-J., Chang, K.-W., Lin, C.-J., Keerthi, S.S., Sundarajan, S.: A dual coordinate descent method for large-scale linear SVM. In: Proceedings of the 25th International Conference on Machine Learning, pp. 408\u2013415. ACM (2008)","DOI":"10.1145\/1390156.1390208"},{"key":"916_CR9","unstructured":"Lacoste-Julien, S., Jaggi, M., Schmidt, M., Pletcher, P.: Block-coordinate Frank\u2013Wolfe optimization for structural SVMs. In: 30th International Conference on Machine Learning (2013)"},{"key":"916_CR10","unstructured":"Lu, Z., Xiao, L.: On the complexity analysis of randomized block-coordinate descent methods. arXiv:1305.4723 (2013)"},{"key":"916_CR11","unstructured":"Lu, Z., Xiao, L.: Randomized block coordinate non-monotone gradient methods for a class of nonlinear programming. arXiv:1306.5918 (2013)"},{"key":"916_CR12","doi-asserted-by":"crossref","unstructured":"Mukherjee, I., Frongillo, R., Canini, K., Singer, Y.: Parallel boosting with momentum. In: Machine Learning and Knowledge Discovery in Databases, vol. 8190, pp 17\u201332. Springer, Heidelberg (2013)","DOI":"10.1007\/978-3-642-40994-3_2"},{"key":"916_CR13","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.jprocont.2012.12.012","volume":"23","author":"I Necoara","year":"2013","unstructured":"Necoara, I., Clipici, D.: Efficient parallel coordinate descent algorithm for convex optimization problems with separable constraints: application to distributed mpc. J. Process Control 23, 243\u2013253 (2013)","journal-title":"J. Process Control"},{"key":"916_CR14","unstructured":"Necoara, I., Nesterov, Y., Glineur, F.: Efficiency of randomized coordinate descent methods on optimization problems with linearly coupled constraints. In: Technical report, vol. 58, pp 2001\u20132012 (2012)"},{"issue":"2","key":"916_CR15","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1137\/100802001","volume":"22","author":"Yu Nesterov","year":"2012","unstructured":"Nesterov, Yu.: Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J Optim 22(2), 341\u2013362 (2012)","journal-title":"SIAM J Optim"},{"key":"916_CR16","unstructured":"Qu, Z., Richt\u00e1rik. P.: Coordinate Descent with Arbitrary Sampling II: Expected Separable Overapproximation. arXiv:1412.8063 (2014)"},{"key":"916_CR17","unstructured":"Qu, Z., Richt\u00e1rik, P., Tak\u00e1\u010d, M., Fercoq, O.: Stochastic Dual Newton Ascent for Empirical Risk Minimization. arXiv:1502.02268"},{"key":"916_CR18","unstructured":"Qu, Z., Richt\u00e1rik, P., Zhang, T.: Randomized Dual Coordinate Ascent with Arbitrary Sampling. arXiv:1411.5873 (2014)"},{"key":"916_CR19","doi-asserted-by":"crossref","unstructured":"Richt\u00e1rik, P., Tak\u00e1\u010d, M.: Efficient serial and parallel coordinate descent methods for huge-scale truss topology design. In: Operations Research Proceedings, pp. 27\u201332. Springer, New York (2012)","DOI":"10.1007\/978-3-642-29210-1_5"},{"key":"916_CR20","doi-asserted-by":"crossref","unstructured":"Richt\u00e1rik, P., Tak\u00e1\u010d, M.: Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. In: Mathematical Programming (2012)","DOI":"10.1007\/s10107-012-0614-z"},{"key":"916_CR21","unstructured":"Richt\u00e1rik, P., Tak\u00e1\u010d, M.: Parallel coordinate descent methods for big data optimization. arXiv:1212.0873 (2012)"},{"key":"916_CR22","unstructured":"Richt\u00e1rik, P., Tak\u00e1\u010d, M.: Distributed coordinate descent method for learning with big data. arXiv:1310.2059 (2013)"},{"key":"916_CR23","first-page":"1865","volume":"12","author":"S Shalev-Shwartz","year":"2011","unstructured":"Shalev-Shwartz, S., Tewari, A.: Stochastic methods for l1-regularized loss minimization. JMLR 12, 1865\u20131892 (2011)","journal-title":"JMLR"},{"key":"916_CR24","unstructured":"Shalev-Shwartz, S., Zhang, T.: Proximal stochastic dual coordinate ascent. arXiv:1211.2717 (2012)"},{"key":"916_CR25","unstructured":"Shalev-Shwartz, S., Zhang, T.: Accelerated mini-batch stochastic dual coordinate ascent. arXiv:1305.2581v1 (2013)"},{"key":"916_CR26","first-page":"567","volume":"14","author":"S Shalev-Shwartz","year":"2013","unstructured":"Shalev-Shwartz, S., Zhang, T.: Stochastic dual coordinate ascent methods for regularized loss minimization. JMLR 14, 567\u2013599 (2013)","journal-title":"JMLR"},{"key":"916_CR27","unstructured":"Tak\u00e1\u010d, M., Bijral, A., Richt\u00e1rik, P., Srebro, N.: Mini-batch primal and dual methods for SVMs. In: ICML (2013)"},{"key":"916_CR28","doi-asserted-by":"crossref","unstructured":"Tappenden, R., Richt\u00e1rik, P., B\u00fcke, B.: Separable approximations and decomposition methods for the augmented Lagrangian. arXiv:1308.6774 (2013)","DOI":"10.1080\/10556788.2014.966824"},{"key":"916_CR29","unstructured":"Tappenden, R., Richt\u00e1rik, P., Gondzio, J.: Inexact coordinate descent: complexity and preconditioning. arXiv:1304.5530 (2013)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-015-0916-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0916-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0916-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T22:02:59Z","timestamp":1566943379000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-015-0916-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,2]]},"references-count":29,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["916"],"URL":"https:\/\/doi.org\/10.1007\/s11590-015-0916-1","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,2]]}}}