{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T03:56:20Z","timestamp":1777607780036,"version":"3.51.4"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p> We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m \u2265 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m \u2265 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1\/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm. <\/jats:p>","DOI":"10.1142\/s0217595915500116","type":"journal-article","created":{"date-parts":[[2014,12,21]],"date-time":"2014-12-21T22:05:14Z","timestamp":1419199514000},"page":"1550011","source":"Crossref","is-referenced-by-count":7,"title":["A Linearized Alternating Direction Method of Multipliers with Substitution Procedure"],"prefix":"10.1142","volume":"32","author":[{"given":"Miantao","family":"Chao","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caozong","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haibin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,6,10]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-66156-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/10556789408805578"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-010-9331-9"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF00247655"},{"key":"rf6","first-page":"17","volume":"2","author":"Gabay D.","year":"1976","journal-title":"Applied Mathematics and Computation"},{"key":"rf7","volume-title":"SIAM Studies in Applied Mathematics","author":"Glowinski R.","year":"1989"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0003-z"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/110822347"},{"key":"rf12","first-page":"2013","volume":"8","author":"Jia Z. H.","year":"2013","journal-title":"Abstract and Applied Analysis"},{"key":"rf13","first-page":"29","volume":"83","author":"Kontogiorgis S.","year":"1998","journal-title":"Mathematical Programming"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1137\/0716071"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(79)90234-8"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1137\/090777761"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595915500116","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:19:22Z","timestamp":1565173162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595915500116"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6]]},"references-count":14,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,6,10]]},"published-print":{"date-parts":[[2015,6]]}},"alternative-id":["10.1142\/S0217595915500116"],"URL":"https:\/\/doi.org\/10.1142\/s0217595915500116","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6]]}}}