{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T14:56:28Z","timestamp":1785855388575,"version":"3.56.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771208"],"award-info":[{"award-number":["11771208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11922111"],"award-info":[{"award-number":["11922111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2021,5]]},"DOI":"10.1007\/s10915-021-01452-9","type":"journal-article","created":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T20:02:47Z","timestamp":1616443367000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["A Golden Ratio Primal\u2013Dual Algorithm for Structured Convex Optimization"],"prefix":"10.1007","volume":"87","author":[{"given":"Xiaokai","family":"Chang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junfeng","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,3,22]]},"reference":[{"key":"1452_CR1","series-title":"CMS Books in Mathematics\/Ouvrages de Math\u00e9matiques de la SMC","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2011","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics\/Ouvrages de Math\u00e9matiques de la SMC, 2nd edn. Springer, Cham (2011)","edition":"2"},{"key":"1452_CR2","series-title":"MOS-SIAM Series on Optimization","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974997","volume-title":"First-Order Methods in Optimization","author":"A Beck","year":"2017","unstructured":"Beck, A.: First-Order Methods in Optimization. MOS-SIAM Series on Optimization. SIAM-Society for Industrial and Applied Mathematics, Philadelphia (2017)"},{"issue":"1","key":"1452_CR3","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"1452_CR4","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BFb0120965","volume":"17","author":"DP Bertsekas","year":"1982","unstructured":"Bertsekas, D.P., Gafni, E.M.: Projection methods for variational inequalities with application to the traffic assignment problem. Math. Program. Stud. 17, 139\u2013159 (1982)","journal-title":"Math. Program. Stud."},{"key":"1452_CR5","doi-asserted-by":"crossref","unstructured":"Bouwmans, T., Aybat, N.S., Zahzah, E.H.: Algorithms for Stable PCA. In: Bouwmans, T., Aybat, N.S., Zahzah, E. (eds.) Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing, chap. 2. CRC Press, Taylor and Francis Group (2016)","DOI":"10.1201\/b20190"},{"issue":"1","key":"1452_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2010","unstructured":"Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1\u2013122 (2010)","journal-title":"Found. Trends Mach. Learn."},{"issue":"4","key":"1452_CR7","doi-asserted-by":"publisher","first-page":"2783","DOI":"10.1137\/17M1134834","volume":"28","author":"A Chambolle","year":"2018","unstructured":"Chambolle, A., Ehrhardt, M.J., Richtarik, P., Schonlieb, C.-B.: Stochastic primal\u2013dual hybrid gradient algorithm with arbitrary sampling and imaging application. SIAM J. Optim. 28(4), 2783\u20132808 (2018)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1452_CR8","doi-asserted-by":"publisher","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\u2013dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"issue":"1\u20132","key":"1452_CR9","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s10107-015-0957-3","volume":"159","author":"A Chambolle","year":"2016","unstructured":"Chambolle, A., Pock, T.: On the ergodic convergence rates of a first-order primal\u2013dual algorithm. Math. Program. 159(1\u20132), 253\u2013287 (2016)","journal-title":"Math. Program."},{"issue":"1","key":"1452_CR10","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1137\/S003614450037906X","volume":"43","author":"S Chen","year":"2001","unstructured":"Chen, S., Saunders, M.A., Donoho, D.L.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129\u2013159 (2001)","journal-title":"SIAM Rev."},{"issue":"4","key":"1452_CR11","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inform. Theory 52(4), 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"1452_CR12","doi-asserted-by":"crossref","unstructured":"Duchi, J., Shalev-Shwartz, S., Singer, Y., Chandra, T.: Efficient projections onto the $$l_1$$-ball for learning in high dimensions. In: The 25th International Conference on Machine Learning, pp. 272\u2013279 (2008)","DOI":"10.1145\/1390156.1390191"},{"issue":"4","key":"1452_CR13","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1137\/09076934X","volume":"3","author":"E Esser","year":"2010","unstructured":"Esser, E., Zhang, X., Chan, T.F.: A general framework for a class of first order primal\u2013dual algorithms for convex optimization in imaging science. SIAM J. Imaging Sci. 3(4), 1015\u20131046 (2010)","journal-title":"SIAM J. Imaging Sci."},{"key":"1452_CR14","doi-asserted-by":"publisher","first-page":"946","DOI":"10.1137\/110853996","volume":"34","author":"M Fazel","year":"2013","unstructured":"Fazel, M., Pong, T.K., Sun, D.F., Tseng, P.: Hankel matrix rank minimization with applications in system identification and realization. SIAM J. Matrix Anal. Appl. 34, 946\u2013977 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1452_CR15","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","volume":"2","author":"D Gabay","year":"1976","unstructured":"Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite-element approximations. Comput. Math. Appl. 2, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"1452_CR16","doi-asserted-by":"crossref","unstructured":"Glowinski, R., Marrocco, A.: Sur l\u2019approximation, par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9, d\u2019une classe de probl\u00e8mes de Dirichlet non lin\u00e9aires. R.A.I.R.O., R2 9(R-2), 41\u201376 (1975)","DOI":"10.1051\/m2an\/197509R200411"},{"issue":"1","key":"1452_CR17","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1137\/110854989","volume":"6","author":"S Hayden","year":"2013","unstructured":"Hayden, S., Stanley, O.: A low patch-rank interpretation of texture. SIAM J. Imaging Sci. 6(1), 226\u2013262 (2013)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"1452_CR18","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1137\/100814494","volume":"5","author":"B He","year":"2012","unstructured":"He, B., Yuan, X.: Convergence analysis of primal\u2013dual algorithms for a saddle-point problem: from contraction perspective. SIAM J. Imaging Sci. 5(1), 119\u2013149 (2012)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1\u20133","key":"1452_CR19","first-page":"293","volume":"55","author":"E Jonathan","year":"1992","unstructured":"Jonathan, E., Dimitri, P.: On the Douglas\u2013Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55(1\u20133), 293\u2013318 (1992)","journal-title":"Math. Program."},{"issue":"6","key":"1452_CR20","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"PL Lions","year":"1979","unstructured":"Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16(6), 964\u2013979 (1979)","journal-title":"SIAM J. Numer. Anal."},{"key":"1452_CR21","unstructured":"Liu, Y., Xu, Y., Yin, W.: Acceleration of primal-dual methods by preconditioning and simple subproblem procedures. arXiv:1811.08937v2 (2018)"},{"key":"1452_CR22","unstructured":"Malitsky, Y.: Golden ratio algorithms for variational inequalities. Math. Program. (to appear)"},{"issue":"1","key":"1452_CR23","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1137\/16M1092015","volume":"28","author":"Y Malitsky","year":"2018","unstructured":"Malitsky, Y., Pock, T.: A first-order primal\u2013dual algorithm with linesearch. SIAM J. Optim. 28(1), 411\u2013432 (2018)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1452_CR24","doi-asserted-by":"publisher","first-page":"1688","DOI":"10.1137\/100801652","volume":"21","author":"RDC Monteiro","year":"2011","unstructured":"Monteiro, R.D.C., Svaiter, B.F.: Complexity of variants of Tseng\u2019s modified FB splitting and Korpelevich\u2019s methods for hemivariational inequalities with applications to saddle-point and convex optimization problems. SIAM J. Optim. 21(4), 1688\u20131720 (2011)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1452_CR25","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/s10957-009-9522-7","volume":"142","author":"A Nedic","year":"2009","unstructured":"Nedic, A., Ozdaglar, A.: Subgradient methods for saddle-point problems. J. Optim. Theory Appl. 142(1), 205\u2013228 (2009)","journal-title":"J. Optim. Theory Appl."},{"issue":"10","key":"1452_CR26","doi-asserted-by":"publisher","first-page":"3941","DOI":"10.1109\/TIP.2013.2264681","volume":"22","author":"D Needell","year":"2013","unstructured":"Needell, D., Ward, R.: Near-optimal compressed sensing guarantees for anisotropic and isotropic total variation minimization. IEEE Trans. Image Process. 22(10), 3941\u20133949 (2013)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"1452_CR27","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1137\/S1052623403425629","volume":"15","author":"A Nemirovski","year":"2006","unstructured":"Nemirovski, A.: Prox-method with rate of convergence O(1\/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex\u2013concave saddle point problems. SIAM J. Optim. 15(1), 229\u2013251 (2006)","journal-title":"SIAM J. Optim."},{"key":"1452_CR28","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1145\/355984.355989","volume":"8","author":"CC Paige","year":"1982","unstructured":"Paige, C.C., Saunders, M.A.: Lsqr: an algorithm for sparselinear equations and sparse least squares. ACM Trans. Math. Soft. 8, 43\u201371 (1982)","journal-title":"ACM Trans. Math. Soft."},{"key":"1452_CR29","doi-asserted-by":"crossref","unstructured":"Pock, T., Chambolle, A.: Diagonal preconditioning for first order primal-dual algorithms in convex optimization. In: IEEE International Conference on Computer Vision, pp. 1762\u20131769 (2011)","DOI":"10.1109\/ICCV.2011.6126441"},{"key":"1452_CR30","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"1","key":"1452_CR31","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1137\/130910774","volume":"24","author":"R Shefi","year":"2014","unstructured":"Shefi, R., Teboulle, M.: Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization. SIAM J. Optim. 24(1), 269\u2013297 (2014)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1452_CR32","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. 58(1), 267\u2013288 (1996)","journal-title":"J. R. Stat. Soc."},{"key":"1452_CR33","volume-title":"Studies in Linear and Nonlinear Programming","author":"H Uzawa","year":"1958","unstructured":"Uzawa, H.: Iterative methods for concave programming. In: Arrow, K.J., Hurwicz, L., Uzawa, H. (eds.) Studies in Linear and Nonlinear Programming. Stanford University Press, Stanford, CA (1958)"},{"issue":"1","key":"1452_CR34","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1137\/090777761","volume":"33","author":"J Yang","year":"2011","unstructured":"Yang, J., Zhang, Y.: Alternating direction algorithms for $$\\ell _1$$-problems in compressive sensing. SIAM J. Sci. Comput. 33(1), 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"1452_CR35","unstructured":"Zhu, M., Chan, T.F.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. In: CAM Report 08-34, UCLA, Los Angeles, CA (2008)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01452-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01452-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01452-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T15:42:33Z","timestamp":1724686953000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01452-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,22]]},"references-count":35,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["1452"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01452-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,22]]},"assertion":[{"value":"5 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"47"}}