{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T04:40:49Z","timestamp":1769575249746,"version":"3.49.0"},"reference-count":31,"publisher":"EDP Sciences","issue":"3","license":[{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"vor","delay-in-days":44,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471102"],"award-info":[{"award-number":["11471102"]}],"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":["12131004"],"award-info":[{"award-number":["12131004"]}],"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":["12071112"],"award-info":[{"award-number":["12071112"]}],"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":["12101195"],"award-info":[{"award-number":["12101195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic research projects for key scientific research projects in Henan Projects of China","award":["No.20ZX001"],"award-info":[{"award-number":["No.20ZX001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,5,9]]},"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p>In the era of big data, much of the data is susceptible to noise with heavy-tailed distribution. Fused Lasso can effectively handle high dimensional sparse data with strong correlation between two adjacent variables under known Gaussian noise. However, it has poor robustness to non-Gaussian noise with heavy-tailed distribution. Robust fused Lasso with<jats:italic>l<\/jats:italic><jats:sub>1<\/jats:sub>norm loss function can overcome the drawback of fused Lasso when noise is heavy-tailed distribution. But the key challenge for solving this model is nonsmoothness and its nonseparability. Therefore, in this paper, we first deform the robust fused Lasso into an easily solvable form, which changes the three-block objective function to a two-block form. Then, we propose an accelerated proximal alternating direction method of multipliers (APADMM) with an additional update step, which is base on a new PADMM that changes the Lagrangian multiplier term update. Furthermore, we give the<jats:italic>O<\/jats:italic>(1\/<jats:italic>K<\/jats:italic>) nonergodic convergence rate analysis of the proposed APADMM. Finally, numerical results show that the proposed new PADMM and APADMM have better performance than other existing ADMM solvers.<\/jats:p>","DOI":"10.1051\/ro\/2023065","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T08:21:57Z","timestamp":1683793317000},"page":"1219-1238","source":"Crossref","is-referenced-by-count":2,"title":["An accelerated proximal alternating direction method of multipliers for robust fused Lasso"],"prefix":"10.1051","volume":"57","author":[{"given":"Yibao","family":"Fan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9859-4040","authenticated-orcid":false,"given":"Youlin","family":"Shang","sequence":"additional","affiliation":[]},{"given":"Zheng-Fen","family":"Jin","sequence":"additional","affiliation":[]},{"given":"Jia","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5305-6708","authenticated-orcid":false,"given":"Roxin","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"Boyd","year":"2010","journal-title":"Found. Trends Mach. Learn."},{"key":"R2","doi-asserted-by":"crossref","first-page":"2179","DOI":"10.1007\/s11425-013-4683-0","volume":"56","author":"Cai","year":"2013","journal-title":"Sci. Chin. Math."},{"key":"R3","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10107-014-0826-5","volume":"155","author":"Chen","year":"2016","journal-title":"Math. Program."},{"key":"R4","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/18.382009","volume":"41","author":"Donoho","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"R5","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/01621459.1983.10477029","volume":"78","author":"Dykstra","year":"1983","journal-title":"J. Am. Stat. Assoc."},{"key":"R6","first-page":"17","volume":"2","author":"Gabay","year":"1976","journal-title":"Comput. Math. App."},{"key":"R7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1051\/m2an\/197509R200411","volume":"9","author":"Glowinski","year":"1975","journal-title":"Revue fran\u00e7aise d\u2019automatique, informatique, recherche op\u00e9rationnelle. Analyse num\u00e9rique"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Golub G.H. and Van Loan C.F., Matrix Computations. JHU Press (2013).","DOI":"10.56021\/9781421407944"},{"key":"R9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40305-021-00368-3","volume":"10","author":"Han","year":"2022","journal-title":"J. Oper. Res. Soc. Chin."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"Hastie T., Tibshirani R., Friedman J.H. and Friedman J.H., The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Vol. 2. Springer (2009).","DOI":"10.1007\/978-0-387-84858-7"},{"key":"R11","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10957-008-9493-0","volume":"141","author":"He","year":"2009","journal-title":"J. Optim. Theory App."},{"key":"R12","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.cam.2013.07.009","volume":"256","author":"Jin","year":"2014","journal-title":"J. Comput. Appl. Math."},{"key":"R13","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/s10915-015-0045-0","volume":"66","author":"Jin","year":"2016","journal-title":"J. Sci. Comput."},{"key":"R14","first-page":"733","volume":"18","author":"Jung","year":"2011","journal-title":"Commun. Stat. App. Methods"},{"key":"R15","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1137\/070690274","volume":"51","author":"Kim","year":"2009","journal-title":"SIAM Rev."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"Kim H.-J., Ollila E. and Koivunen V., New robust Lasso method based on ranks, in 2015 23rd European Signal Processing Conference (EUSIPCO). IEEE (2015) 699\u2013703.","DOI":"10.1109\/EUSIPCO.2015.7362473"},{"key":"R17","first-page":"73","volume":"87","author":"Lemaire","year":"1989","journal-title":"Int. Ser. Numer. Math."},{"key":"R18","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s10915-018-0893-5","volume":"79","author":"Li","year":"2019","journal-title":"J. Sci. Comput."},{"key":"R19","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.csda.2014.05.017","volume":"79","author":"Li","year":"2014","journal-title":"Comput. Stat. Data Anal."},{"key":"R20","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1137\/140999025","volume":"26","author":"Li","year":"2016","journal-title":"SIAM J. Optim."},{"key":"R21","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1137\/17M1136390","volume":"28","author":"Li","year":"2018","journal-title":"SIAM J. Optim."},{"key":"R22","first-page":"97","volume":"8","author":"Liu","year":"2018","journal-title":"Numer. Algebra"},{"key":"R23","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1137\/14095697X","volume":"8","author":"Ouyang","year":"2015","journal-title":"SIAM J. Imaging Sci."},{"key":"R24","doi-asserted-by":"crossref","first-page":"2922","DOI":"10.1214\/08-AOS665","volume":"37","author":"Rinaldo","year":"2009","journal-title":"Ann. Stat."},{"key":"R25","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.cor.2016.11.004","volume":"81","author":"Sebastio","year":"2017","journal-title":"Comput. Oper. Res."},{"key":"R26","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.cam.2004.11.030","volume":"181","author":"Shang","year":"2005","journal-title":"J. Comput. Appl. Math."},{"key":"R27","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"R28","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/j.1467-9868.2005.00490.x","volume":"67","author":"Tibshirani","year":"2005","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"},{"key":"R29","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.jmva.2013.04.001","volume":"120","author":"Wang","year":"2013","journal-title":"J. Multivariate Anal."},{"key":"R30","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1198\/073500106000000251","volume":"25","author":"Wang","year":"2007","journal-title":"J. Bus. Econ. Stat."},{"key":"R31","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1007\/s00180-012-0373-6","volume":"28","author":"Wang","year":"2013","journal-title":"Comput. Stat."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023065\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,20]],"date-time":"2024-10-20T05:55:26Z","timestamp":1729403726000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023065"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5]]},"references-count":31,"journal-issue":{"issue":"3"},"alternative-id":["ro230087"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2023065","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"2804-7303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5]]}}}