{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T05:16:28Z","timestamp":1788412588374,"version":"build-2803163510"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1613996"],"award-info":[{"award-number":["DMS 1613996"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in a landmark 1976 paper: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions (like the Euclidean norm) whose minimizers are isolated nonsmooth points.<\/jats:p>","DOI":"10.1137\/17m1121883","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T11:53:02Z","timestamp":1525780382000},"page":"1301-1311","source":"Crossref","is-referenced-by-count":11,"title":["Nonsmooth Variants of Powell's BFGS Convergence Theorem"],"prefix":"10.1137","volume":"28","author":[{"given":"Jiayi","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. S.","family":"Lewis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"atypb1","unstructured":"A. Asl and M.L. Overton,\n                      Analysis of the Gradient Method with an Armijo-Wolfe Line Search on a Class of Nonsmooth Convex Functions\n                      , preprint, arXiv:1711.08517, 2017."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0522-2"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0802003"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"J.B. Hiriart-Urruty and C. Lemare\u0301chal,\n                      Convex Analysis and Minimization Algorithms I\n                      , Springer, Berlin, 1993.","DOI":"10.1007\/978-3-662-02796-7"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0514-2"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-014-0622-7"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00939948"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0421-7"},{"key":"atypb9","unstructured":"J. Nocedal and S.J. Wright,\n                      Numerical Optimization\n                      , 2nd ed., Springer Ser. Oper. Res. Financ. Eng., Springer, New York, 2006."},{"key":"atypb10","first-page":"53","year":"1976","journal-title":"RI"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s101070050115"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/060658370"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-96-08416-1"},{"key":"atypb14","first-page":"965","volume":"21","author":"Yan M.","year":"2014","journal-title":"J. Convex Anal."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1121883","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:03:13Z","timestamp":1787338993000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1121883"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1121883"],"URL":"https:\/\/doi.org\/10.1137\/17m1121883","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}