{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T14:50:50Z","timestamp":1772981450577,"version":"3.50.1"},"reference-count":44,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["Y760"],"award-info":[{"award-number":["Y760"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,3,31]]},"DOI":"10.1137\/23m1575469","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T08:20:24Z","timestamp":1772094024000},"page":"320-349","source":"Crossref","is-referenced-by-count":0,"title":["Convergence Regions of Alternating Minimization Algorithms for Dictionary Learning"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0434-8982","authenticated-orcid":true,"given":"Simon","family":"Ruetz","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universit\u00e4t Innsbruck, Innsbruck, 6020 Austria."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4873-5570","authenticated-orcid":true,"given":"Karin","family":"Schnass","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universit\u00e4t Innsbruck, Innsbruck, 6020 Austria."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2026,2,26]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/140979861"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2614684"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2006.881199"},{"key":"ref4","volume-title":"COLT 2015","author":"Arora S.","year":"2015"},{"key":"ref5","volume-title":"COLT 2014","author":"Arora S.","year":"2014"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746605"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.862083"},{"key":"ref8","volume-title":"Advances in Neural Information Processing Systems 30 (NIPS 2017)","author":"Chatterji N.","year":"2017"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/1657381"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000000067"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.1999.760624"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1038\/381607a0"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2472522"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2048466"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2006.03.036"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1162\/089976603762552951"},{"key":"ref18","unstructured":"Y. LeCun, C. Cortes, and C. Burges, MNIST handwritten digit database, AT & T Labs [Online]. Available: https:\/\/web.archive.org\/web\/20250105151917\/https:\/\/yann.lecun.com\/exdb\/mnist\/, 2010."},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015826"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2011.156"},{"key":"ref21","first-page":"19","volume":"11","author":"Mairal J.","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2017.03.020"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792240406"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2022.3167313"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iaad008"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/ACSSC.1993.342465"},{"key":"ref27","unstructured":"Q. Qu, Y. Zhai, X. Li, Y. Zhang, and Z. Zhu, Geometric analysis of nonconvex optimization landscapes for overcomplete learning, in International Conference on Learning Representations, 2020."},{"key":"ref28","unstructured":"R. Rubinstein, M. Zibulevsky, and M. Elad, Efficient Implementation of the K-SVD Algorithm Using Batch Orthogonal Matching Pursuit, Technical report 40(8), CS Technion, 2008."},{"key":"ref29","unstructured":"S. Ruetz, Adapted Variable Density Subsampling for Compressed Sensing, arXiv:2206.13796, 2022."},{"key":"ref30","unstructured":"S. Ruetz, Compressed Sensing and Dictionary Learning with Non-Uniform Support Distribution, Ph.D. thesis, University of Innsbruck, 2022."},{"key":"ref31","volume-title":"in preparation","author":"Ruetz S.","year":"2023"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/20M1386384"},{"key":"ref33","unstructured":"S. Ruetz and K. Schnass, Non-asymptotic Bounds for Inclusion Probabilities in Rejective Sampling, arXiv:2212.09391, 2022."},{"key":"ref34","unstructured":"S. Ruetz and K. Schnass, Convergence of Alternating Minimisation Algorithms for Dictionary Learning, arXiv:2304.01768v2, 2023."},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2012.2209871"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.01.005"},{"key":"ref37","first-page":"1211","volume":"16","author":"Schnass K.","year":"2015","journal-title":"J. Mach. Learn. Res."},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2016.08.002"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2010.2040671"},{"key":"ref40","volume-title":"COLT 2012","author":"Spielman D.","year":"2012"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2632162"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2632149"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2014.2345761"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-011-9099-z"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T08:20:25Z","timestamp":1772958025000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1575469"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,26]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3,31]]}},"alternative-id":["10.1137\/23M1575469"],"URL":"https:\/\/doi.org\/10.1137\/23m1575469","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,26]]}}}