{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:45:40Z","timestamp":1753886740185,"version":"3.41.2"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,12,22]],"date-time":"2011-12-22T00:00:00Z","timestamp":1324512000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171138","11171049"],"award-info":[{"award-number":["11171138","11171049"]}],"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":["11171138","11171049"],"award-info":[{"award-number":["11171138","11171049"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>A decomposition algorithm based on proximal bundle\u2010type method with inexact data is presented for minimizing an unconstrained nonsmooth convex function <jats:italic>f<\/jats:italic>. At each iteration, only the approximate evaluation of <jats:italic>f<\/jats:italic> and its approximate subgradients are required which make the algorithm easier to implement. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem. Numerical tests emphasize the theoretical findings.<\/jats:p>","DOI":"10.1155\/2012\/215160","type":"journal-article","created":{"date-parts":[[2011,12,22]],"date-time":"2011-12-22T21:02:02Z","timestamp":1324587722000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors"],"prefix":"10.1155","volume":"2012","author":[{"given":"Yuan","family":"Lu","sequence":"first","affiliation":[]},{"given":"Li-Ping","family":"Pang","sequence":"additional","affiliation":[]},{"given":"Jie","family":"Shen","sequence":"additional","affiliation":[]},{"given":"Xi-Jun","family":"Liang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,12,22]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1625"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0314056"},{"key":"e_1_2_6_3_2","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1007\/BFb0121157","article-title":"Numerical methods for nondifferentiable convex optimization","author":"Auslender A.","year":"1987","journal-title":"Mathematical Programming Study"},{"volume-title":"Convex Analysis and Minimization Algo-Rithms","year":"1993","author":"Hiriart-Urruty J.-B.","key":"e_1_2_6_4_2"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02243-6"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45780-7_11"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499350967"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-005-0630-3"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.01.003"},{"key":"e_1_2_6_10_2","first-page":"563","article-title":"Proximal points are on the fast track","volume":"9","author":"Mifflin R.","year":"2002","journal-title":"Journal of Convex Analysis"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000005046.70410.02"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585170"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011259017643"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/215160.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/215160.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/215160","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:58:18Z","timestamp":1718089098000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/215160"}},"subtitle":[],"editor":[{"given":"Chein-Shan","family":"Liu","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2011,12,22]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/215160"],"URL":"https:\/\/doi.org\/10.1155\/2012\/215160","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2011,12,22]]},"assertion":[{"value":"2011-07-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-25","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-12-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"215160"}}