{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:39:33Z","timestamp":1740145173000,"version":"3.37.3"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T00:00:00Z","timestamp":1547683200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T00:00:00Z","timestamp":1547683200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s11590-019-01388-y","type":"journal-article","created":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T03:51:29Z","timestamp":1547697089000},"page":"1071-1088","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Alternating forward\u2013backward splitting for linearly constrained optimization problems"],"prefix":"10.1007","volume":"14","author":[{"given":"Cesare","family":"Molinari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8551-0522","authenticated-orcid":false,"given":"Juan","family":"Peypouquet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fernando","family":"Roldan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,1,17]]},"reference":[{"key":"1388_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5802\/afst.541","volume":"2","author":"F Acker","year":"1980","unstructured":"Acker, F., Prestel, M.A.: Convergence d\u2019un sch\u00e9ma de minimisation altern\u00e9e. Ann. Facult\u00e9 des Sci. Toulouse V S\u00e9r. Math. 2, 1\u20139 (1980)","journal-title":"Ann. Facult\u00e9 des Sci. Toulouse V S\u00e9r. Math."},{"issue":"3","key":"1388_CR2","first-page":"485","volume":"15","author":"H Attouch","year":"2008","unstructured":"Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Alternating proximal algorithms for weakly coupled convex minimization problems. Applications to dynamical games and PDE\u2019s. J. Convex Anal. 15(3), 485\u2013506 (2008)","journal-title":"J. Convex Anal."},{"key":"1388_CR3","first-page":"125","volume":"34","author":"H Attouch","year":"1986","unstructured":"Attouch, H., Br\u00e9zis, H.: Duality for the sum of convex functions in general Banach spaces. Asp. Math. Appl. J. Barroso Ed. 34, 125\u2013133 (1986)","journal-title":"Asp. Math. Appl. J. Barroso Ed."},{"issue":"18","key":"1388_CR4","doi-asserted-by":"crossref","first-page":"7455","DOI":"10.1016\/j.na.2011.07.066","volume":"74","author":"H Attouch","year":"2011","unstructured":"Attouch, H., Cabot, A., Frankel, P., Peypouquet, J.: Alternating proximal algorithms for constrained variational inequalities. Application to domain decomposition for PDE\u2019s. Nonlinear Anal. 74(18), 7455\u20137473 (2011)","journal-title":"Nonlinear Anal."},{"key":"1388_CR5","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1137\/100789464","volume":"21","author":"H Attouch","year":"2011","unstructured":"Attouch, H., Czarnecki, M.-O., Peypouquet, J.: Prox-penalization and splitting methods for constrained variational problems. SIAM J. Optim. 21, 149\u2013173 (2011)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1388_CR6","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1137\/110820300","volume":"21","author":"H Attouch","year":"2011","unstructured":"Attouch, H., Czarnecki, M.-O., Peypouquet, J.: Coupling forward\u2013backward with penalty schemes and parallel splitting for constrained variational inequalities. SIAM J. Optim. 21(4), 1251\u20131274 (2011)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1388_CR7","doi-asserted-by":"crossref","first-page":"1824","DOI":"10.1137\/15M1046095","volume":"26","author":"H Attouch","year":"2016","unstructured":"Attouch, H., Peypouquet, J.: The rate of convergence of Nesterov\u2019s accelerated forward\u2013backward method is actually faster than 1\/k2. SIAM J. Optim. 26(3), 1824\u20131834 (2016)","journal-title":"SIAM J. Optim."},{"key":"1388_CR8","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1137\/060657248","volume":"18","author":"H Attouch","year":"2007","unstructured":"Attouch, H., Redont, P., Soubeyran, A.: A new class of alternating proximal minimization algorithms with costs-to-move. SIAM J. Optim. 18, 1061\u20131081 (2007)","journal-title":"SIAM J. Optim."},{"key":"1388_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00939042","volume":"55","author":"A Auslender","year":"1987","unstructured":"Auslender, A., Crouzeix, J.P., Fedit, P.: Penalty-proximal methods in convex programming. J. Optim. Theory Appl. 55, 1\u201321 (1987)","journal-title":"J. Optim. Theory Appl."},{"key":"1388_CR10","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.na.2004.07.054","volume":"60","author":"HH Bauschke","year":"2005","unstructured":"Bauschke, H.H., Combettes, P.L., Reich, S.: The asymptotic behavior of the composition of two resolvents. Nonlinear Anal. 60, 283\u2013301 (2005)","journal-title":"Nonlinear Anal."},{"issue":"11","key":"1388_CR11","doi-asserted-by":"crossref","first-page":"2419","DOI":"10.1109\/TIP.2009.2028250","volume":"18","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419\u20132434 (2009)","journal-title":"IEEE Trans. Image Process."},{"key":"1388_CR12","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s00245-012-9174-0","volume":"66","author":"M Bildhauer","year":"2012","unstructured":"Bildhauer, M., Fuchs, M.: A variational approach to the denoising of images based on different variants of the TV-regularization. Appl. Math. Optim. 66, 331\u2013361 (2012)","journal-title":"Appl. Math. Optim."},{"issue":"3","key":"1388_CR13","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1137\/11083277X","volume":"50","author":"S Bertels","year":"2012","unstructured":"Bertels, S.: Total variation minimization with finite elements: convergence and iterative solution. SIAM J. Numer. Anal. 50(3), 1162\u20131180 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"1388_CR14","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1080\/02331934.2013.855210","volume":"64","author":"L Brice\u00f1o-Arias","year":"2015","unstructured":"Brice\u00f1o-Arias, L.: Forward-Douglas\u2013Rachford splitting and forward-partial inverse method for solving monotone inclusions. Optimization 64(5), 1239\u20131261 (2015)","journal-title":"Optimization"},{"key":"1388_CR15","unstructured":"Brice\u00f1o-Arias, L., L\u00f3pez, S.: A projected primal-dual splitting for solving constrained monotone inclusions. arXiv:1805.11687v1 [math.OC]"},{"issue":"2","key":"1388_CR16","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1137\/S105262340343467X","volume":"15","author":"A Cabot","year":"2005","unstructured":"Cabot, A.: Proximal point algorithm controlled by a slowly vanishing term: applications to hierarchical minimization. SIAM J. Optim. 15(2), 555\u2013572 (2005)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1388_CR17","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.acha.2010.10.002","volume":"31","author":"EJ Cand\u00e8s","year":"2011","unstructured":"Cand\u00e8s, E.J., Eldar, Y.C., Needell, D., Randall, P.: Compressed sensing with coherent and redundant dictionaries. Appl. Comput. Harmon. Anal. 31(1), 59\u201373 (2011)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"1388_CR18","unstructured":"Carter, J.L.: Dual methods for total variation-based image restoration. Ph.D. Thesis, UCLA (2001)"},{"key":"1388_CR19","first-page":"536","volume":"25","author":"AL Cauchy","year":"1847","unstructured":"Cauchy, A.L.: M\u00e9thode g\u00e9n\u00e9rale pour la r\u00e9solution des syst\u00e8mes d\u2019\u00e9quations simultan\u00e9es. C. R. Acad. Sci. Paris 25, 536\u2013538 (1847)","journal-title":"C. R. Acad. Sci. Paris"},{"issue":"3","key":"1388_CR20","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1007\/s10957-015-0746-4","volume":"166","author":"A Chambolle","year":"2015","unstructured":"Chambolle, A., Dossal, C.: On the convergence of the iterates of the \u201cfast iterative shrinkage\/thresholding algorithm\u201d. J. Optim. Theory Appl. 166(3), 968\u2013982 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"1388_CR21","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s002110050258","volume":"76","author":"A Chambolle","year":"1997","unstructured":"Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numer. Math. 76, 167\u2013188 (1997)","journal-title":"Numer. Math."},{"issue":"1","key":"1388_CR22","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(1), 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"1388_CR23","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/0-387-28831-7_2","volume-title":"Handbook of mathematical models in computer vision","author":"T Chan","year":"2006","unstructured":"Chan, T., Esedoglu, S., Park, F., Yip, A.: Total variation image restoration: overview and recent developments. In: Paragios, N., Chen, Y., Faugeras, O.D. (eds.) Handbook of mathematical models in computer vision, pp. 17\u201331. Springer, New York (2006)"},{"issue":"6","key":"1388_CR24","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1137\/S1064827596299767","volume":"20","author":"TF Chan","year":"1999","unstructured":"Chan, T.F., Golub, G.H., Mulet, P.: A nonlinear primal-dual method for total variation-based image restoration. SIAM J. Sci. Comput. 20(6), 1964\u20131977 (1999)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1\u20133","key":"1388_CR25","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01582566","volume":"64","author":"G Chen","year":"1994","unstructured":"Chen, G., Teboulle, M.: A proximal-based decomposition method for convex minimization problems. Math. Program. 64(1\u20133), 81\u2013101 (1994)","journal-title":"Math. Program."},{"issue":"3\u20134","key":"1388_CR26","first-page":"727","volume":"16","author":"PL Combettes","year":"2009","unstructured":"Combettes, P.L.: Iterative construction of the resolvent of a sum of maximal monotone operators. J. Convex Anal. 16(3\u20134), 727\u2013748 (2009)","journal-title":"J. Convex Anal."},{"key":"1388_CR27","doi-asserted-by":"crossref","unstructured":"Combettes, P.L., Pesquet, J.C.: A proximal decomposition method for solving convex variational inverse problems. Inverse Probl. 24(26) (2008)","DOI":"10.1088\/0266-5611\/24\/6\/065014"},{"key":"1388_CR28","doi-asserted-by":"crossref","unstructured":"Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing. Fixed-point algorithms for inverse problems in science and engineering. In: Bauschke, H.H., Burachik, R.S.S., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (eds.) Springer Optimization and Its Applications, vol. 49, pp. 185\u2013212. Springer, New York (2011)","DOI":"10.1007\/978-1-4419-9569-8_10"},{"issue":"2","key":"1388_CR29","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s11228-011-0191-y","volume":"20","author":"PL Combettes","year":"2012","unstructured":"Combettes, P.L., Pesquet, J.C.: Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set Valued Var. Anal. 20(2), 307\u2013330 (2012)","journal-title":"Set Valued Var. Anal."},{"issue":"4","key":"1388_CR30","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/050626090","volume":"4","author":"PL Combettes","year":"2005","unstructured":"Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward\u2013backward splitting. Multiscale Model. Simul. 4(4), 1168\u20131200 (2005)","journal-title":"Multiscale Model. Simul."},{"issue":"2","key":"1388_CR31","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1007\/s10957-012-0245-9","volume":"158","author":"L Condat","year":"2013","unstructured":"Condat, L.: A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms. J. Optim. Theory Appl. 158(2), 460\u2013479 (2013)","journal-title":"J. Optim. Theory Appl."},{"issue":"11","key":"1388_CR32","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1002\/cpa.20042","volume":"57","author":"I Daubechies","year":"2004","unstructured":"Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413\u20131457 (2004)","journal-title":"Commun. Pure Appl. Math."},{"issue":"1\u20132","key":"1388_CR33","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10107-014-0809-6","volume":"148","author":"W De Oliveira","year":"2014","unstructured":"De Oliveira, W., Sagastiz\u00e1bal, C., Lemar\u00e9chal, C.: Convex proximal bundle methods in depth: a unified analysis for inexact oracles. Math. Program. Ser. B 148(1\u20132), 241\u2013277 (2014)","journal-title":"Math. Program. Ser. B"},{"issue":"5","key":"1388_CR34","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1137\/S003614299528701X","volume":"34","author":"DC Dobson","year":"1997","unstructured":"Dobson, D.C., Vogel, C.R.: Convergence of an iterative method for total variation denoising. SIAM J. Numer. Anal. 34(5), 1779\u20131791 (1997)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1388_CR35","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1090\/S0002-9947-1956-0084194-4","volume":"82","author":"J Douglas","year":"1956","unstructured":"Douglas, J., Rachford, H.H.: On the numerical solution of heat conduction problems in two and three space variables. Trans. Am. Math. Soc. 82(2), 421\u2013439 (1956)","journal-title":"Trans. Am. Math. Soc."},{"issue":"2","key":"1388_CR36","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10589-009-9274-1","volume":"46","author":"J Eckstein","year":"2010","unstructured":"Eckstein, J., Silva, P.J.S.: Proximal methods for nonlinear programming: double regularization and inexact subproblems. Comput. Optim. Appl. 46(2), 279\u2013304 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"1388_CR37","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10851-017-0754-0","volume":"60","author":"G Garrigos","year":"2017","unstructured":"Garrigos, G., Rosasco, L., Villa, S.: Iterative regularization via dual diagonal descent. J. Math. Imaging Vis. 60, 189\u2013215 (2017). https:\/\/doi.org\/10.1007\/s10851-017-0754-0","journal-title":"J. Math. Imaging Vis."},{"issue":"5","key":"1388_CR38","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1090\/S0002-9904-1964-11178-2","volume":"70","author":"AA Goldstein","year":"1964","unstructured":"Goldstein, A.A.: Convex programming in Hilbert space. Bull. Am. Math. Soc. 70(5), 709\u2013710 (1964)","journal-title":"Bull. Am. Math. Soc."},{"issue":"2","key":"1388_CR39","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"1388_CR40","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10589-016-9861-x","volume":"66","author":"S Gonz\u00e1lez-Andrade","year":"2017","unstructured":"Gonz\u00e1lez-Andrade, S.: A preconditioned descent algorithm for variational inequalities of the second kind involving the $$p$$-Laplacian operator. Comput. Optim. Appl. 66(1), 123\u2013162 (2017)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"1388_CR41","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s11228-016-0394-3","volume":"26","author":"W Hare","year":"2018","unstructured":"Hare, W., Planiden, C.: Computing proximal points of convex functions with inexact subgradients. Set Valued Var. Anal. 26(3), 469\u2013492 (2018)","journal-title":"Set Valued Var. Anal."},{"issue":"1","key":"1388_CR42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10589-015-9762-4","volume":"63","author":"W Hare","year":"2016","unstructured":"Hare, W., Sagastiz\u00e1bal, C., Solodov, M.: A proximal bundle method for nonsmooth nonconvex functions with inexact information. Comput. Optim. Appl. 63(1), 1\u201328 (2016)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"1388_CR43","doi-asserted-by":"crossref","first-page":"2446","DOI":"10.1137\/110854539","volume":"50","author":"MJ Lai","year":"2012","unstructured":"Lai, M.J., Messi, L.M.: Piecewise linear approximation of the continuous Rudin\u2013Osher\u2013Fatemi model for image denoising. SIAM J. Numer. Anal. 50(5), 2446\u20132466 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"1388_CR44","doi-asserted-by":"crossref","unstructured":"Levitin, E.S., Polyak, B.T.: Constrained minimization problems. USSR Comput. Math. Math. Phys. 6, 1\u201350 (1966) (English translation of original paper in Zh. Vychisl. Mat. Fiz. 6, 787\u2013823, 1965)","DOI":"10.1016\/0041-5553(66)90114-5"},{"key":"1388_CR45","first-page":"154","volume":"4","author":"B Martinet","year":"1970","unstructured":"Martinet, B.: R\u00e9gularisation d\u2019in\u00e9quations variationnelles par approximations successives. Rev. Fran\u00e7aise Informat. Recherche Op\u00e9rationnelle 4, 154\u2013158 (1970)","journal-title":"Rev. Fran\u00e7aise Informat. Recherche Op\u00e9rationnelle"},{"issue":"2","key":"1388_CR46","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s10957-018-1265-x","volume":"177","author":"C Molinari","year":"2018","unstructured":"Molinari, C., Peypouquet, J.: Lagrangian penalization algorithm with parallel forward\u2013backward splitting. J. Optim. Theory Appl. 177(2), 413\u2013447 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"1388_CR47","volume-title":"Fonctionnelles Convexes","author":"JJ Moreau","year":"1967","unstructured":"Moreau, J.J.: Fonctionnelles Convexes. Cours Coll\u00e8ge de France, Paris (1967)"},{"key":"1388_CR48","first-page":"372","volume":"27","author":"Y Nesterov","year":"1983","unstructured":"Nesterov, Y.: A method of solving a convex programming problem with convergence rate $$O(1\/k^2)$$. Sov. Math. Dokl. 27, 372\u2013376 (1983)","journal-title":"Sov. Math. Dokl."},{"key":"1388_CR49","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1090\/S0002-9904-1967-11761-0","volume":"73","author":"Z Opial","year":"1967","unstructured":"Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73, 591\u2013597 (1967)","journal-title":"Bull. Am. Math. Soc."},{"issue":"3","key":"1388_CR50","first-page":"123","volume":"1","author":"N Parikh","year":"2014","unstructured":"Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 123\u2013231 (2014)","journal-title":"Found. Trends Optim."},{"key":"1388_CR51","doi-asserted-by":"crossref","unstructured":"Peypouquet, J.: Convex Optimization in Normed Spaces. Theory, Methods and Examples. With a Foreword by Hedy Attouch. Springer, Berlin (2015)","DOI":"10.1007\/978-3-319-13710-0"},{"issue":"2","key":"1388_CR52","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s12215-017-0318-6","volume":"67","author":"D Reem","year":"2018","unstructured":"Reem, D., Reich, S.: Solutions to inexact resolvent inclusion problems with applications to nonlinear analysis and optimization. Rend. Circ. Mat. Palermo (2) 67(2), 337\u2013371 (2018)","journal-title":"Rend. Circ. Mat. Palermo (2)"},{"key":"1388_CR53","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"1388_CR54","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877\u2013898 (1976)","journal-title":"SIAM J. Control Optim."},{"key":"1388_CR55","doi-asserted-by":"crossref","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. Physica D 60, 259\u2013268 (1992)","journal-title":"Physica D"},{"issue":"9","key":"1388_CR56","doi-asserted-by":"crossref","first-page":"2016","DOI":"10.1016\/j.na.2006.02.039","volume":"66","author":"J Shen","year":"2007","unstructured":"Shen, J., Xia, Z.Q., Pang, L.P.: A proximal bundle method with inexact data for convex nondifferentiable minimization. Nonlinear Anal. 66(9), 2016\u20132027 (2007)","journal-title":"Nonlinear Anal."},{"key":"1388_CR57","first-page":"2510","volume":"27","author":"W Su","year":"2014","unstructured":"Su, W., Boyd, S., Cand\u00e8s, E.J.: A differential equation for modeling Nesterov\u2019s accelerated gradient method: theory and insights. NIPS 27, 2510\u20132518 (2014)","journal-title":"NIPS"},{"key":"1388_CR58","doi-asserted-by":"crossref","unstructured":"Tai, X.C., Wu, C.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. In: Tai, X.C., Moerken, K., Lysaker, M., Lie, K.A. (eds.) Scale space and variational methods in computer vision, pp. 502\u2013513 (2009)","DOI":"10.1007\/978-3-642-02256-2_42"},{"issue":"1","key":"1388_CR59","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/0917016","volume":"17","author":"CR Vogel","year":"1996","unstructured":"Vogel, C.R., Oman, M.E.: Iterative methods for total variation denoising. SIAM J. Sci. Comput. 17(1), 227\u2013238 (1996)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1388_CR60","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1007\/s10957-014-0526-6","volume":"164","author":"BC Vu","year":"2015","unstructured":"Vu, B.C.: A splitting algorithm for coupled system of primal-dual monotone inclusions. J. Optim. Theory Appl. 164(3), 993\u20131025 (2015)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"1388_CR61","doi-asserted-by":"crossref","first-page":"237","DOI":"10.3934\/ipi.2011.5.237","volume":"5","author":"C Wu","year":"2011","unstructured":"Wu, C., Zhang, J., Tai, X.C.: Augmented Lagrangian method for total variation restoration with non-quadratic fidelity. Inverse Probl. Imaging 5(1), 237\u2013261 (2011)","journal-title":"Inverse Probl. Imaging"},{"key":"1388_CR62","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s10589-008-9225-2","volume":"47","author":"M Zhu","year":"2010","unstructured":"Zhu, M., Wright, S.J., Chan, T.F.: Duality-based algorithms for total-variation-regularized image restoration. Comput. Optim. Appl. 47, 377\u2013400 (2010)","journal-title":"Comput. Optim. Appl."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-019-01388-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-019-01388-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-019-01388-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,10]],"date-time":"2022-09-10T12:22:55Z","timestamp":1662812575000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-019-01388-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,17]]},"references-count":62,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["1388"],"URL":"https:\/\/doi.org\/10.1007\/s11590-019-01388-y","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"type":"print","value":"1862-4472"},{"type":"electronic","value":"1862-4480"}],"subject":[],"published":{"date-parts":[[2019,1,17]]},"assertion":[{"value":"26 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}