{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T20:29:28Z","timestamp":1773692968039,"version":"3.50.1"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,10,21]],"date-time":"2012-10-21T00:00:00Z","timestamp":1350777600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1007\/s10898-012-9999-8","type":"journal-article","created":{"date-parts":[[2012,10,20]],"date-time":"2012-10-20T06:18:09Z","timestamp":1350713889000},"page":"1419-1428","source":"Crossref","is-referenced-by-count":24,"title":["An improved first-order primal-dual algorithm with a new correction step"],"prefix":"10.1007","volume":"57","author":[{"given":"Xingju","family":"Cai","sequence":"first","affiliation":[]},{"given":"Deren","family":"Han","sequence":"additional","affiliation":[]},{"given":"Lingling","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,10,21]]},"reference":[{"key":"9999_CR1","unstructured":"Arrow, K.J., Hurwicz, L., Uzawa, H.: With contributions by H.B. Chenery, S.M. Johnson, S. Karlin, T. Marschak, and R.M. Solow. Studies in Linear and Non-Linear Programming, volume II of Stanford Mathematical Studies in the Social Science. Stanford Unversity Press, Stanford, (1958)"},{"key":"9999_CR2","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0024-3795(82)90149-5","volume":"42","author":"Y. Censor","year":"1982","unstructured":"Censor Y., Elfving T.: New methods for linear inequalities. Linear Algebra It\u2019s Appl. 42, 199\u2013211 (1982)","journal-title":"Linear Algebra It\u2019s Appl."},{"key":"9999_CR3","doi-asserted-by":"crossref","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, 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"9999_CR4","doi-asserted-by":"crossref","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, 1015\u20131046 (2010)","journal-title":"SIAM J. Imaging Sci."},{"key":"9999_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0041-5553(67)90113-9","volume":"7","author":"L.G. Gubin","year":"1967","unstructured":"Gubin L.G., Polyak B.T., Raik E.V.: The method of projections for finding the common point of convex sets. USSR Comput. Math. Math. Phys. 7, 1\u201324 (1967)","journal-title":"USSR Comput. Math. Math. Phys."},{"issue":"2","key":"9999_CR6","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00211-008-0181-7","volume":"111","author":"D. Han","year":"2008","unstructured":"Han D., Xu W., Yang H.: An operator splitting method for variational inequalities with partially unknown mappings. Numer. Math. 111(2), 207\u2013237 (2008)","journal-title":"Numer. Math."},{"issue":"1","key":"9999_CR7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s101070100280","volume":"92","author":"B. He","year":"2002","unstructured":"He B., Liao L.Z., Han D., Yang H.: A new inexact alternating directions method for monotone variational inequalities. Math. Progr. 92(1), 103\u2013118 (2002)","journal-title":"Math. Progr."},{"issue":"2","key":"9999_CR8","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/110822347","volume":"22","author":"B. He","year":"2012","unstructured":"He B., Tao M., Yuan X.: Alternating direction method with gaussian back substitution for separable convex programming. SIAM J. Optim. 22(2), 313\u2013340 (2012)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"9999_CR9","doi-asserted-by":"crossref","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-rachford alternating direction method. SIAM J. Numer. Anal. 50(2), 700\u2013709 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"9999_CR10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1137\/100814494","volume":"5","author":"B.S. He","year":"2012","unstructured":"He B.S., Yuan X.M.: Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective. SIAM J. Imaging Sci. 5, 119\u2013149 (2012)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"9999_CR11","doi-asserted-by":"crossref","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":"9999_CR12","unstructured":"Zhu, M.Q., Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. CAM reports 08\u201334, UCLA, (2008)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9999-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-012-9999-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9999-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:59:03Z","timestamp":1559264343000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-012-9999-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,21]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["9999"],"URL":"https:\/\/doi.org\/10.1007\/s10898-012-9999-8","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,21]]}}}