{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:25:35Z","timestamp":1766067935291},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T00:00:00Z","timestamp":1708732800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T00:00:00Z","timestamp":1708732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10851-024-01173-2","type":"journal-article","created":{"date-parts":[[2024,2,24]],"date-time":"2024-02-24T12:02:09Z","timestamp":1708776129000},"page":"231-245","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Prediction\u2013Correction Primal\u2013Dual Hybrid Gradient Algorithm for Solving Convex Minimization Problems with Linear Constraints"],"prefix":"10.1007","volume":"66","author":[{"given":"Fahimeh","family":"Alipour","sequence":"first","affiliation":[]},{"given":"Mohammad Reza","family":"Eslahchi","sequence":"additional","affiliation":[]},{"given":"Masoud","family":"Hajarian","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,2,24]]},"reference":[{"key":"1173_CR1","doi-asserted-by":"crossref","unstructured":"Bai, J., Hager, W. W., Zhang, H.: An inexact accelerated stochastic ADMM for separable convex optimization. Comput. Optim. Appl. 1\u201340 (2022)","DOI":"10.1007\/s10589-021-00338-8"},{"key":"1173_CR2","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. SIAM, Philadelphia (2017)"},{"key":"1173_CR3","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1007\/s10851-011-0324-9","volume":"44","author":"S Bonettini","year":"2012","unstructured":"Bonettini, S., Ruggiero, V.: On the convergence of primal\u2013dual hybrid gradient algorithms for total variation image restoration. J. Math. Imaging Vis. 44, 236\u2013253 (2012)","journal-title":"J. Math. Imaging Vis."},{"key":"1173_CR4","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"JF Cai","year":"2010","unstructured":"Cai, J.F., Cand\u00e8s, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20, 1956\u20131982 (2010)","journal-title":"SIAM J. Optim."},{"key":"1173_CR5","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1007\/s10898-012-9999-8","volume":"57","author":"XJ Cai","year":"2013","unstructured":"Cai, X.J., Han, D.R., Xu, L.L.: An improved first-order primal\u2013dual algorithm with a new correction step. J. Glob. Optim. 57, 1419\u20131428 (2013)","journal-title":"J. Glob. Optim."},{"key":"1173_CR6","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"EJ Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9, 717\u2013772 (2009)","journal-title":"Found. Comput. Math."},{"key":"1173_CR7","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 algorithms for convex problem with applications to imaging. J. Math. Imaging Vis. 40, 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"1173_CR8","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. Prog. Ser. A 159, 253\u2013287 (2016)","journal-title":"Math. Prog. Ser. A"},{"key":"1173_CR9","doi-asserted-by":"crossref","unstructured":"Chan, R.H., Ma, S.Q., Yang, J.F.: Inertial primal\u2013dual algorithms for structured convex optimization. arXiv:1409.2992 (2014)","DOI":"10.1155\/2014\/396753"},{"key":"1173_CR10","doi-asserted-by":"publisher","first-page":"1779","DOI":"10.1137\/130919362","volume":"24","author":"Y Chen","year":"2014","unstructured":"Chen, Y., Lan, G., Ouyang, Y.: Optimal primal\u2013dual methods for a class of saddle point problems. SIAM J. Optim. 24, 1779\u20131814 (2014)","journal-title":"SIAM J. Optim."},{"key":"1173_CR11","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1137\/S003614450037906X","volume":"43","author":"SS Chen","year":"2001","unstructured":"Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43, 129\u2013159 (2001)","journal-title":"SIAM Rev."},{"key":"1173_CR12","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1137\/09076934X","volume":"3","author":"E Esser","year":"2010","unstructured":"Esser, E., Zhang, X.Q., 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, 1015\u20131046 (2010)","journal-title":"SIAM J. Imaging Sci."},{"key":"1173_CR13","unstructured":"Goldstein, T., Li, M., Yuan, X.: Adaptive primal-dual splitting methods for statistical learning and image processing. In: Cortes, C., Lawrence, N.D., Lee, D.D., Sugiyama, M., Garnett, R. (eds.) Advances in Neural Information Processing Systems 28, pp. 2089\u20132097. Curran Associates, Inc. (2015). http:\/\/papers.nips.cc\/paper\/5723-adaptive-primal-dual-splitting-methods-for-statistical-learningand-image-processing.pdf"},{"key":"1173_CR14","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718874","volume-title":"Deblurring Images: Matrices Spectra and Filtering","author":"PC Hansen","year":"2006","unstructured":"Hansen, P.C., Nagy, J.G., O\u2019leary, D.P.: Deblurring Images: Matrices Spectra and Filtering. SIAM, Philadelphia (2006)"},{"key":"1173_CR15","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s10851-017-0709-5","volume":"58","author":"BS He","year":"2017","unstructured":"He, B.S., Ma, F., Yuan, X.M.: An algorithmic framework of generalized primal\u2013dual hybrid gradient methods for saddle point problems. J. Math. Imaging Vis. 58, 279\u2013293 (2017)","journal-title":"J. Math. Imaging Vis."},{"key":"1173_CR16","doi-asserted-by":"crossref","unstructured":"He, B.S., Xu, M.H., Yuan, X.M.: Solving large-scale least squares semidefinite programming by alternating direction methods. SIAM J. Matrix Anal. Appl. 3, 136\u2013152 (2011)","DOI":"10.1137\/090768813"},{"key":"1173_CR17","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1137\/100814494","volume":"5","author":"BS He","year":"2012","unstructured":"He, B.S., Yuan, X.M.: Convergence analysis of primal\u2013dual algorithms for a saddle-point problem: from contraction perspective. SIAM J. Imaging Sci. 5, 119\u2013149 (2012)","journal-title":"SIAM J. Imaging Sci."},{"key":"1173_CR18","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10589-013-9564-5","volume":"56","author":"BS He","year":"2013","unstructured":"He, B.S., Yuan, X.M., Zhang, W.X.: A customized proximal point algorithm for convex minimization with linear constraints. Comput. Optim. Appl. 56, 559\u2013572 (2013)","journal-title":"Comput. Optim. Appl."},{"key":"1173_CR19","doi-asserted-by":"publisher","first-page":"2526","DOI":"10.1137\/140963467","volume":"7","author":"BS He","year":"2014","unstructured":"He, B.S., You, Y.F., Yuan, X.M.: On the convergence of primal\u2013dual hybrid gradient algorithm. SIAM J. Imaging Sci. 7, 2526\u20132537 (2014)","journal-title":"SIAM J. Imaging Sci."},{"key":"1173_CR20","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/s10898-016-0437-1","volume":"66","author":"HJ He","year":"2016","unstructured":"He, H.J., Desai, J., Wang, K.: A primal\u2013dual prediction\u2013correction algorithm for saddle point optimization. J. Glob. Optim. 66, 573\u2013583 (2016)","journal-title":"J. Glob. Optim."},{"key":"1173_CR21","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"MR Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appli. 4, 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appli."},{"issue":"6","key":"1173_CR22","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.3934\/ipi.2020058","volume":"14","author":"L Hu","year":"2020","unstructured":"Hu, L., Zhang, W., Cai, X., Han, D.: A parallel operator splitting algorithm for solving constrained total-variation retinex. Inver. Prob. Imaging 14(6), 1135\u20131156 (2020)","journal-title":"Inver. Prob. Imaging"},{"key":"1173_CR23","first-page":"154","volume":"126","author":"B Martinet","year":"1970","unstructured":"Martinet, B.: R\u00e9gularision d\u2019in\u00e9quations variationnelles par approximations successive. Revue Francaise d\u2019Automatique et Informatique Recherche Op\u00e9rationnelle 126, 154\u2013159 (1970)","journal-title":"Revue Francaise d\u2019Automatique et Informatique Recherche Op\u00e9rationnelle"},{"key":"1173_CR24","doi-asserted-by":"publisher","first-page":"896","DOI":"10.1007\/s40314-016-0371-3","volume":"37","author":"F Ma","year":"2018","unstructured":"Ma, F., Ni, M.F.: A class of customized proximal point algorithms for linearly constrained convex optimization. Comput. Appl. Math. 37, 896\u2013911 (2018)","journal-title":"Comput. Appl. Math."},{"key":"1173_CR25","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1007\/s11075-018-0618-8","volume":"82","author":"F Ma","year":"2019","unstructured":"Ma, F., Bi, Y., Gao, B.: A prediction\u2013correction-based primal\u2013dual hybrid gradient method for linearly constrained convex minimization. Numer. Algor. 82, 641\u2013662 (2019)","journal-title":"Numer. Algor."},{"key":"1173_CR26","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s10107-009-0306-5","volume":"128","author":"SQ Ma","year":"2011","unstructured":"Ma, S.Q., Goldfarb, D., Chen, L.: Fixed point and Bregman iterative methods for matrix rank minimization. Math. Prog. Ser. A. 128, 321\u2013353 (2011)","journal-title":"Math. Prog. Ser. A."},{"issue":"4","key":"1173_CR27","doi-asserted-by":"publisher","first-page":"2140","DOI":"10.1137\/17M1113138","volume":"10","author":"MK Ng","year":"2017","unstructured":"Ng, M.K., Ngan, H.Y., Yuan, X., Zhang, W.: Lattice-based patterned fabric inspection by using total variation with sparsity and low-rank representations. SIAM J. Imaging Sci. 10(4), 2140\u20132164 (2017)","journal-title":"SIAM J. Imaging Sci."},{"key":"1173_CR28","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1561\/2400000003","volume":"1","author":"N Parikh","year":"2014","unstructured":"Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1, 127\u2013239 (2014)","journal-title":"Found. Trends Optim."},{"key":"1173_CR29","first-page":"283","volume-title":"Optimization","author":"MJD Powell","year":"1969","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283\u2013298. Academic Press, New York (1969)"},{"key":"1173_CR30","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259\u2013268 (1992)","journal-title":"Phys. D"},{"key":"1173_CR31","doi-asserted-by":"publisher","first-page":"743","DOI":"10.3934\/jimo.2014.10.743","volume":"10","author":"Y Shen","year":"2014","unstructured":"Shen, Y., Zhang, W., He, B.S.: Relaxed augmented Lagrangian-based proximal point algorithms for convex optimization with linear constraints. J. Ind. Manag. Optim. 10, 743\u2013759 (2014)","journal-title":"J. Ind. Manag. Optim."},{"key":"1173_CR32","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511730344","volume-title":"Sparse Image and Signal Processing, Wavelets, Curvelets, Morphological Diversity","author":"JL Starck","year":"2010","unstructured":"Starck, J.L., Murtagh, F., Fadili, J.M.: Sparse Image and Signal Processing, Wavelets, Curvelets, Morphological Diversity. Cambridge University Press, Cambridge (2010)"},{"key":"1173_CR33","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.na.2007.11.031","volume":"70","author":"W Takahashi","year":"2008","unstructured":"Takahashi, W., Zembayashi, K.: Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. Nonlinear Anal. 70, 45\u201357 (2008)","journal-title":"Nonlinear Anal."},{"key":"1173_CR34","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1090\/S0025-5718-2012-02598-1","volume":"82","author":"JF Yang","year":"2013","unstructured":"Yang, J.F., Yuan, X.M.: Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization. Math. Comp. 82, 301\u2013329 (2013)","journal-title":"Math. Comp."},{"key":"1173_CR35","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1137\/070703983","volume":"1","author":"W Yin","year":"2008","unstructured":"Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for $$l_1$$-minimization with applications to compressed sensing. SIAM J. Imaging Sci. 1, 143\u2013168 (2008)","journal-title":"SIAM J. Imaging Sci."},{"key":"1173_CR36","doi-asserted-by":"crossref","unstructured":"Zhang, X., Kong, Y., Liu, S., Shen, Y.: A relaxed parameter condition for the primal\u2013dual hybrid gradient method for saddle-point problem. J. Ind. Manag. Optim. 19(3), 1595\u20131610 (2023)","DOI":"10.3934\/jimo.2022008"},{"key":"1173_CR37","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/s10915-010-9408-8","volume":"46","author":"XQ Zhang","year":"2011","unstructured":"Zhang, X.Q., Burger, M., Osher, S.: A unified primal\u2013dual algorithm framework based on Bregman iteration. J. Sci. Comput. 46, 20\u201346 (2011)","journal-title":"J. Sci. Comput."},{"key":"1173_CR38","unstructured":"Zhu, M., Chan, T.F.: An efficient primal\u2013dual hybrid gradient algorithm for total variation image restoration, CAM Report 08-34, UCLA USA (2008)"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-024-01173-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-024-01173-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-024-01173-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T10:08:17Z","timestamp":1715854097000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-024-01173-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,24]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["1173"],"URL":"https:\/\/doi.org\/10.1007\/s10851-024-01173-2","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,24]]},"assertion":[{"value":"13 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}