{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:37:25Z","timestamp":1787341045541,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1527809"],"award-info":[{"award-number":["CCF-1527809"]}],"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>We introduce a quasi-Newton method with block updates called block BFGS. We show that this method, performed with inexact Armijo--Wolfe line searches, converges globally and $Q$-superlinearly under the same convexity assumptions as BFGS. We also show that block BFGS is globally convergent to a stationary point when applied to nonconvex functions with bounded Hessian, and discuss other modifications for nonconvex minimization. Numerical experiments comparing block BFGS, BFGS, and gradient descent are presented.<\/jats:p>","DOI":"10.1137\/16m1092106","type":"journal-article","created":{"date-parts":[[2018,4,24]],"date-time":"2018-04-24T14:25:03Z","timestamp":1524579903000},"page":"1205-1231","source":"Crossref","is-referenced-by-count":14,"title":["Block BFGS Methods"],"prefix":"10.1137","volume":"28","author":[{"given":"Wenbo","family":"Gao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donald","family":"Goldfarb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,24]]},"reference":[{"key":"atypb1","first-page":"147","volume":"10","author":"Andrei N.","year":"2008","journal-title":"Adv. Model. Optim."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/140954362"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0724077"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1145\/1961189.1961199"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1974-0343581-1"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100263"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1970-0258249-6"},{"key":"atypb8","first-page":"1869","volume":"48","author":"Gower R.","year":"2016","journal-title":"JMLR: Workshop Conf. Proc."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01407874"},{"key":"atypb10","unstructured":"W. Hager,\n                      COAP Test Problems: A Collection of Optimization Test Problems\n                      ,http:\/\/users.clas.ufl.edu\/hager\/coap\/Pages\/matlabpage.html(2016)."},{"key":"atypb11","unstructured":"R. A. Horn and C. R. Johnson,\n                      Matrix Analysis\n                      , 2nd ed., Cambridge University Press, Cambridge, 2013."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00540-9"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499354242"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01589116"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1080\/10556789908805768"},{"key":"atypb16","first-page":"53","author":"M. J.","year":"1976","journal-title":"RI"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01588967"},{"key":"atypb18","unstructured":"M. Schmidt,\n                      MinFUNC\n                      ,http:\/\/www.cs.ubc.ca\/~schmidtm\/Software\/minFunc.html(2005)."},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"R. Schnabel,\n                      Quasi-Newton Methods using Multiple Secant Quotations\n                      , Technical report CU-CS-247-83, University of Colorado at Boulder, Boulder, CO, 1983.","DOI":"10.21236\/ADA131444"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1145\/3104990"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1092106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:03:03Z","timestamp":1787338983000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1092106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1092106"],"URL":"https:\/\/doi.org\/10.1137\/16m1092106","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}