{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:43:42Z","timestamp":1753886622658,"version":"3.41.2"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,12,27]],"date-time":"2012-12-27T00:00:00Z","timestamp":1356566400000},"content-version":"vor","delay-in-days":361,"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":["11071087","11126147","11201197"],"award-info":[{"award-number":["11071087","11126147","11201197"]}],"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":["11071087","11126147","11201197"],"award-info":[{"award-number":["11071087","11126147","11201197"]}],"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":["11071087","11126147","11201197"],"award-info":[{"award-number":["11071087","11126147","11201197"]}],"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>Recently, Xiao et al. proposed a nonsmooth equations\u2010based method to solve the <jats:italic>\u2113<\/jats:italic><jats:sub>1<\/jats:sub>\u2010norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations\u2010based algorithms for solving <jats:italic>\u2113<\/jats:italic><jats:sub>1<\/jats:sub>\u2010norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms.<\/jats:p>","DOI":"10.1155\/2012\/139609","type":"journal-article","created":{"date-parts":[[2012,12,27]],"date-time":"2012-12-27T21:00:41Z","timestamp":1356642041000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New Nonsmooth Equations\u2010Based Algorithms for <i>\u2113<\/i><sub>1<\/sub>\u2010Norm Minimization and Applications"],"prefix":"10.1155","volume":"2012","author":[{"given":"Lei","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,12,27]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"e_1_2_6_2_2","doi-asserted-by":"crossref","unstructured":"EladM. 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