{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T19:35:39Z","timestamp":1792697739083,"version":"4.5.0"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["I1148"],"award-info":[{"award-number":["I1148"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires an update of only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not require any additional matrix-vector multiplications. We prove convergence of the proposed method under standard assumptions. We also show an ergodic $O(1\/N)$ rate of convergence for our method. In the case when one or both of the prox-functions are strongly convex, we modify our basic method to get a better convergence rate. Finally, we propose a linesearch for a saddle-point problem with an additional smooth term. Several numerical experiments confirm the efficiency of our proposed methods.<\/jats:p>","DOI":"10.1137\/16m1092015","type":"journal-article","created":{"date-parts":[[2018,2,13]],"date-time":"2018-02-13T14:14:48Z","timestamp":1518531288000},"page":"411-432","source":"Crossref","is-referenced-by-count":110,"title":["A First-Order Primal-Dual Algorithm with Linesearch"],"prefix":"10.1137","volume":"28","author":[{"given":"Yura","family":"Malitsky","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Pock","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,2,13]]},"reference":[{"key":"atypb1","first-page":"37","author":"Agarwal A.","year":"2010","journal-title":"Canada"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"H. H. Bauschke and P. L. Combettes,\n                      Convex Analysis and Monotone Operator Theory in Hilbert Spaces\n                      , Springer, New York, 2011.","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0251-1"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0957-3"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S096249291600009X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0245-9"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra,\n                      Efficient projections onto the\n                      $\\ell_1$-ball for learning in high dimensions\n                      , in Proceedings of the 25th International Conference on Machine Learning, 2008, pp. 272-279.","DOI":"10.1145\/1390156.1390191"},{"key":"atypb9","first-page":"2089","author":"Goldstein T.","year":"2015","journal-title":"Advances in Neural Information Processing Systems"},{"key":"atypb10","unstructured":"T. Goldstein, M. Li, X. Yuan, E. Esser, and R. Baraniuk,\n                      Adaptive Primal-Dual Hybrid Gradient Methods for Saddle-Point Problems\n                      , preprint,arXiv:1305.0546, 2013."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004603514434"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/100814494"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2014.2377273"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2017.1300899"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/14097238X"},{"key":"atypb16","first-page":"1762","author":"Pock T.","year":"2011","journal-title":"Spain"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998338806"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-011-9254-8"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2009.2016892"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1092015","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:15:17Z","timestamp":1787336117000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1092015"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1092015"],"URL":"https:\/\/doi.org\/10.1137\/16m1092015","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}