{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T10:28:38Z","timestamp":1720002518601},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1016\/j.amc.2020.125719","type":"journal-article","created":{"date-parts":[[2020,10,21]],"date-time":"2020-10-21T15:56:09Z","timestamp":1603295769000},"page":"125719","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":3,"special_numbering":"C","title":["New convergence results for the inexact variable metric forward\u2013backward method"],"prefix":"10.1016","volume":"392","author":[{"given":"S.","family":"Bonettini","sequence":"first","affiliation":[]},{"given":"M.","family":"Prato","sequence":"additional","affiliation":[]},{"given":"S.","family":"Rebegoldi","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"5","key":"10.1016\/j.amc.2020.125719_bib0001","doi-asserted-by":"crossref","first-page":"055005","DOI":"10.1088\/1361-6420\/aa5bfd","article-title":"On the convergence of a linesearch based proximal-gradient method for nonconvex optimization","volume":"33","author":"Bonettini","year":"2017","journal-title":"Inverse Probl."},{"issue":"1\u20132","key":"10.1016\/j.amc.2020.125719_bib0002","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","article-title":"Convergence of descent methods for semi\u2013algebraic and tame problems: proximal algorithms, forward\u2013backward splitting, and regularized Gauss\u2013Seidel methods","volume":"137","author":"Attouch","year":"2013","journal-title":"Math. Program."},{"issue":"9","key":"10.1016\/j.amc.2020.125719_bib0003","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1080\/02331934.2012.733883","article-title":"Variable metric forward-backward splitting with applications to monotone inclusions in duality","volume":"63","author":"Combettes","year":"2014","journal-title":"Optimization"},{"issue":"3","key":"10.1016\/j.amc.2020.125719_bib0004","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s10898-016-0405-9","article-title":"A block coordinate variable metric forward-backward algorithm","volume":"66","author":"Chouzenoux","year":"2016","journal-title":"J. Global Optim."},{"issue":"1\u20132","key":"10.1016\/j.amc.2020.125719_bib0005","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","article-title":"Proximal alternating linearized minimization for nonconvex and nonsmooth problems","volume":"146","author":"Bolte","year":"2014","journal-title":"Math. Program."},{"issue":"2","key":"10.1016\/j.amc.2020.125719_bib0006","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1137\/15M1019325","article-title":"Variable metric inexact line\u2013search based methods for nonsmooth optimization","volume":"26","author":"Bonettini","year":"2016","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.amc.2020.125719_bib0007","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1007\/s10957-014-0642-3","article-title":"Splitting methods with variable metric for Kurdyka\u2013\u0141ojasiewicz functions and general convergence rates","volume":"165","author":"Frankel","year":"2015","journal-title":"J. Opt. Theory Appl."},{"key":"10.1016\/j.amc.2020.125719_bib0008","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.amc.2014.12.079","article-title":"On some steplength approaches for proximal algorithms","volume":"253","author":"Porta","year":"2015","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"10.1016\/j.amc.2020.125719_bib0009","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1137\/16M1073741","article-title":"The variable metric forward-backward splitting algorithm under mild differentiability assumptions","volume":"27","author":"Salzo","year":"2017","journal-title":"SIAM J. Optim."},{"issue":"4","key":"10.1016\/j.amc.2020.125719_bib0010","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/050626090","article-title":"Signal recovery by proximal forward-backward splitting","volume":"4","author":"Combettes","year":"2005","journal-title":"Multiscale Model. Simul."},{"key":"10.1016\/j.amc.2020.125719_bib0011","series-title":"Nonlinear Programming","author":"Bertsekas","year":"1999"},{"issue":"1","key":"10.1016\/j.amc.2020.125719_bib0012","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage\u2013thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM J. Imaging Sci."},{"issue":"2","key":"10.1016\/j.amc.2020.125719_bib0013","doi-asserted-by":"crossref","first-page":"1388","DOI":"10.1137\/130942954","article-title":"iPiano: Inertial proximal algorithm for non-convex optimization","volume":"7","author":"Ochs","year":"2014","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"10.1016\/j.amc.2020.125719_bib0014","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1137\/17M1124085","article-title":"Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano","volume":"29","author":"Ochs","year":"2019","journal-title":"SIAM J. Optim."},{"issue":"1\u20132","key":"10.1016\/j.amc.2020.125719_bib0015","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s10107-007-0170-0","article-title":"A coordinate gradient descent method for nonsmooth separable minimization","volume":"117","author":"Tseng","year":"2009","journal-title":"Math. Program."},{"issue":"4","key":"10.1016\/j.amc.2020.125719_bib0016","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1137\/050644641","article-title":"The \u0141ojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems","volume":"17","author":"Bolte","year":"2007","journal-title":"SIAM J. Optim."},{"issue":"6","key":"10.1016\/j.amc.2020.125719_bib0017","doi-asserted-by":"crossref","DOI":"10.1090\/S0002-9947-09-05048-X","article-title":"Characterizations of \u0141ojasiewicz inequalities: subgradient flows, talweg, convexity","volume":"362","author":"Bolte","year":"2010","journal-title":"Trans. Am. Math. Soc."},{"key":"10.1016\/j.amc.2020.125719_bib0018","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1137\/060670080","article-title":"Clarke subgradients of stratifiable functions","volume":"18","author":"Bolte","year":"2007","journal-title":"SIAM J. Optim."},{"issue":"1","key":"10.1016\/j.amc.2020.125719_bib0019","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10957-013-0465-7","article-title":"Variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function","volume":"162","author":"Chouzenoux","year":"2014","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.amc.2020.125719_bib0020","doi-asserted-by":"crossref","unstructured":"S. Bonettini, M. Prato, S. Rebegoldi, Convergence of inexact forward-backward algorithms using the forward-backward envelope, 2020, (http:\/\/www.optimization-online.org\/DB_HTML\/2020\/02\/7644.html). Preprint.","DOI":"10.1137\/19M1254155"},{"issue":"4","key":"10.1016\/j.amc.2020.125719_bib0021","first-page":"1167","article-title":"Inexact and accelerated proximal point algorithms","volume":"19","author":"Salzo","year":"2012","journal-title":"J. Convex Anal."},{"issue":"3","key":"10.1016\/j.amc.2020.125719_bib0022","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1137\/110844805","article-title":"Accelerated and inexact forward-backward algorithms","volume":"23","author":"Villa","year":"2013","journal-title":"SIAM J. Optim."},{"issue":"5","key":"10.1016\/j.amc.2020.125719_bib0023","doi-asserted-by":"crossref","first-page":"A3180","DOI":"10.1137\/17M116001X","article-title":"Inertial variable metric techniques for the inexact forward\u2013backward algorithm","volume":"40","author":"Bonettini","year":"2018","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"10.1016\/j.amc.2020.125719_bib0024","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s10589-019-00059-z","article-title":"Inexact successive quadratic approximation for regularized optimization","volume":"72","author":"Lee","year":"2019","journal-title":"Comput. Optim. Appl."},{"key":"10.1016\/j.amc.2020.125719_bib0025","series-title":"Variational Analysis","volume":"317","author":"Rockafellar","year":"1998"},{"key":"10.1016\/j.amc.2020.125719_bib0026","series-title":"Convex Analysis in General Vector Spaces","author":"Zalinescu","year":"2002"},{"key":"10.1016\/j.amc.2020.125719_bib0027","series-title":"Les \u00c9quations aux D\u00e9riv\u00e9es Partielles","first-page":"87","article-title":"Une propri\u00e9t\u00e9 topologique des sous-ensembles analytiques r\u00e9els","author":"\u0141ojasiewicz","year":"1963"},{"issue":"4","key":"10.1016\/j.amc.2020.125719_bib0028","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/imanum\/23.4.539","article-title":"Inexact spectral projected gradient methods on convex sets","volume":"23","author":"Birgin","year":"2003","journal-title":"IMA J. Numer. Anal."},{"issue":"1\u20134","key":"10.1016\/j.amc.2020.125719_bib0029","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","article-title":"Nonlinear total variation based noise removal algorithms","volume":"60","author":"Rudin","year":"1992","journal-title":"J. Phys. D."},{"key":"10.1016\/j.amc.2020.125719_bib0030","first-page":"2777","article-title":"Structured variable selection with sparsity inducing norms","author":"Jenatton","year":"2011","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"10.1016\/j.amc.2020.125719_bib0031","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.amc.2017.09.001","article-title":"A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography","volume":"318","author":"Bubba","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2020.125719_bib0032","series-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"Bauschke","year":"2011"},{"issue":"8","key":"10.1016\/j.amc.2020.125719_bib0033","doi-asserted-by":"crossref","first-page":"085009","DOI":"10.1088\/1361-6420\/aa790a","article-title":"A comparison of edge\u2013preserving approaches for differential interference contrast microscopy","volume":"33","author":"Rebegoldi","year":"2017","journal-title":"Inverse Probl."},{"issue":"1","key":"10.1016\/j.amc.2020.125719_bib0034","doi-asserted-by":"crossref","first-page":"124678","DOI":"10.1016\/j.amc.2019.124678","article-title":"ACQUIRE: an inexact iteratively reweighted norm approach for TV\u2013based Poisson image restoration","volume":"364","author":"di Serafino","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2020.125719_bib0035","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10589-018-0011-5","article-title":"A block coordinate variable metric linesearch based proximal gradient method","volume":"71","author":"Bonettini","year":"2018","journal-title":"Comput. Optim. Appl."},{"issue":"1-2","key":"10.1016\/j.amc.2020.125719_bib0036","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10107-007-0133-5","article-title":"On the convergence of the proximal algorithm for nonsmooth functions involving analytic features","volume":"116","author":"Attouch","year":"2009","journal-title":"Math. Program."},{"key":"10.1016\/j.amc.2020.125719_bib0037","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/s10957-018-01452-0","article-title":"Non-smooth non-convex Bregman minimization: unification and new algorithms","volume":"181","author":"Ochs","year":"2019","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.amc.2020.125719_bib0038","series-title":"Pattern Recognition","first-page":"271","article-title":"Revisiting loss-specific training of filter-based MRFs for image restoration","author":"Chen","year":"2013"},{"key":"10.1016\/j.amc.2020.125719_bib0039","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1007\/s10957-015-0746-4","article-title":"On the convergence of the iterates of the \u201cFast Iterative Shrinkage\/Thresholding Algorithm\u201d","volume":"166","author":"Chambolle","year":"2015","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"10.1016\/j.amc.2020.125719_bib0040","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1287\/moor.2016.0817","article-title":"A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications","volume":"4","author":"Bauschke","year":"2017","journal-title":"Math. Oper. Res."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S009630032030672X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S009630032030672X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T22:01:52Z","timestamp":1698271312000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S009630032030672X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":40,"alternative-id":["S009630032030672X"],"URL":"https:\/\/doi.org\/10.1016\/j.amc.2020.125719","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2021,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"New convergence results for the inexact variable metric forward\u2013backward method","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.amc.2020.125719","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2020 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}],"article-number":"125719"}}