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method for solving two-block separable convex problems and its convergence is well understood. When either the involved number of blocks is more than two, or there is a nonconvex function, or there is a nonseparable structure, ADMM or its directly extend version may not converge. In this paper, we proposed an ADMM-based algorithm for nonconvex multiblock optimization problems with a nonseparable structure. We show that any cluster point of the iterative sequence generated by the proposed algorithm is a critical point, under mild condition. Furthermore, we establish the strong convergence of the whole sequence, under the condition that the potential function satisfies the Kurdyka\u2013\u0141ojasiewicz property. This provides the theoretical basis for the application of the proposed ADMM in the practice. Finally, we give some preliminary numerical results to show the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.1155\/2020\/6237942","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T18:31:43Z","timestamp":1582741903000},"page":"1-14","source":"Crossref","is-referenced-by-count":6,"title":["Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4763-9533","authenticated-orcid":true,"given":"Miantao","family":"Chao","sequence":"first","affiliation":[{"name":"Department of Mathematics, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhao","family":"Deng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8048-7397","authenticated-orcid":true,"given":"Jinbao","family":"Jian","sequence":"additional","affiliation":[{"name":"Guangxi University for Nationalities, Nanning, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/197509r200411"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(76)90003-1"},{"key":"3","first-page":"825","volume":"30","year":"2014","journal-title":"Optimization Methods and Software"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2016.1227432"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-017-0631-6"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1137\/140990309"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-018-0034-y"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/140998135"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-017-9367-6"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-018-0757-z"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1142\/s0217595917500300"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1137\/15m1027528"},{"key":"14","year":"1998"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90040-7"},{"key":"16","first-page":"1705","volume":"6","year":"2005","journal-title":"Journal of Machine Learning Research"},{"key":"17","year":"2006"},{"key":"18","first-page":"3319","volume":"362","year":"2010","journal-title":"Transactions of the American Mathematical Society"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.5802\/aif.1638"},{"key":"20","first-page":"87","volume-title":"Une propri\u00e9t\u00e9 topologique des sous-ensembles analytiques r\u00e9els","year":"1963"},{"key":"21","first-page":"575","volume":"43","year":"1993","journal-title":"Annales de l\u2019institut Fourier"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0484-9"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1100.0449"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1137\/050644641"},{"key":"25","year":"2004"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1109\/tnnls.2012.2197412"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6237942.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6237942.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6237942.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T18:31:46Z","timestamp":1582741906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/6237942\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,26]]},"references-count":25,"alternative-id":["6237942","6237942"],"URL":"https:\/\/doi.org\/10.1155\/2020\/6237942","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,26]]}}}