{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T16:05:51Z","timestamp":1775145951290,"version":"3.50.1"},"reference-count":25,"publisher":"MIT Press - Journals","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2008,3]]},"abstract":"<jats:p> The constrained L<jats:sub>1<\/jats:sub> estimation is an attractive alternative to both the unconstrained L<jats:sub>1<\/jats:sub> estimation and the least square estimation. In this letter, we propose a cooperative recurrent neural network (CRNN) for solving L<jats:sub>1<\/jats:sub> estimation problems with general linear constraints. The proposed CRNN model combines four individual neural network models automatically and is suitable for parallel implementation. As a special case, the proposed CRNN includes two existing neural networks for solving unconstrained and constrained L<jats:sub>1<\/jats:sub> estimation problems, respectively. Unlike existing neural networks, with penalty parameters, for solving the constrained L<jats:sub>1<\/jats:sub> estimation problem, the proposed CRNN is guaranteed to converge globally to the exact optimal solution without any additional condition. Compared with conventional numerical algorithms, the proposed CRNN has a low computational complexity and can deal with the L<jats:sub>1<\/jats:sub> estimation problem with degeneracy. Several applied examples show that the proposed CRNN can obtain more accurate estimates than several existing algorithms. <\/jats:p>","DOI":"10.1162\/neco.2007.10-06-376","type":"journal-article","created":{"date-parts":[[2007,11,28]],"date-time":"2007-11-28T17:58:18Z","timestamp":1196272698000},"page":"844-872","source":"Crossref","is-referenced-by-count":14,"title":["A Cooperative Recurrent Neural Network for Solving <i>L<\/i><sub>1<\/sub> Estimation Problems with General Linear Constraints"],"prefix":"10.1162","volume":"20","author":[{"given":"Youshen","family":"Xia","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer Science, Fuzhou University, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed S.","family":"Kamel","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Waterloo, Canada."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-2312(98)00013-7"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1137\/0715015"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1006\/dspr.2001.0409"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1109\/5.784227"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1109\/78.295211"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1109\/78.845914"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1109\/82.193316"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/0925-2312(94)E0063-W"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2002.1011217"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cds:20010418"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.813832"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1109\/78.157191"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015826"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495293160"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.820672"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0121126"},{"key":"p_25","doi-asserted-by":"publisher","DOI":"10.1109\/29.21687"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2003.822284"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1996.8.5.1061"},{"key":"p_28","doi-asserted-by":"publisher","DOI":"10.1109\/72.572118"},{"key":"p_29","doi-asserted-by":"publisher","DOI":"10.1109\/72.991418"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2004.838929"},{"key":"p_33","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-2312(97)00082-9"},{"key":"p_34","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2004.824252"},{"key":"p_35","doi-asserted-by":"publisher","DOI":"10.1109\/JOE.1987.1145232"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco.2007.10-06-376","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:35:28Z","timestamp":1615584928000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/20\/3\/844-872\/7293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,3]]}},"alternative-id":["10.1162\/neco.2007.10-06-376"],"URL":"https:\/\/doi.org\/10.1162\/neco.2007.10-06-376","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}