{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:30:00Z","timestamp":1787333400261,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,8]]},"abstract":"<jats:p>This paper explores the global convergence of the least-change secant method proposed by Dennis and Wolkowicz[SIAM J. Numer. Anal., 30 (1993), pp. 1291--1314]. This method is a member of the Broyden family, but it doesn't necessarily belong to the Broyden convex family. Furthermore, it can be very close to the DFP method. We will prove that this method, with the Wolfe line search on uniformly convex objective functions, is globally convergent.<\/jats:p>","DOI":"10.1137\/s1052623495280378","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"813-832","source":"Crossref","is-referenced-by-count":1,"title":["Global Analysis of the Dennis--Wolkowicz Least-Change Secant Algorithm"],"prefix":"10.1137","volume":"8","author":[{"given":"Lixing","family":"Han","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanghui","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0802026"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0726042"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0724077"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01681328"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1145\/355958.355965"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971200"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0730067"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0801002"},{"key":"R9","volume-title":"Practical methods of optimization","author":"Fletcher R.","year":"1987"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"JorgeNocedal, Theory of algorithms for unconstrained optimization, Acta Numer., Cambridge Univ. Press, Cambridge, 1992, 199\u201324293b:90087","DOI":"10.1017\/S0962492900002270"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.20.5.845"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580654"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/12.2.171"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF00933517"},{"key":"R15","unstructured":"M. J. D. Powell,\n                      Some global convergence properties of a variable metric algorithm for minimization without exact line searches\n                      , in Nonlinear Programming, SIAM\u2013AMS Proceedings, Vol. IX, R. W. Cottle and C. E. Lemke, eds., AMS, Providence, RI, 1976."},{"key":"R16","unstructured":"J. Werner,\n                      Global Convergence of Quasi\u2010Newton Methods with Practical Line Searches\n                      , Technical Report, NAM\u2010Bericht 67, Institut f\u00fcr Numerische und Angewandte Mathematik der Universit\u00e4t G\u00f6ttingen, Germany, 1989."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1287\/moor.19.4.815"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/8.4.487"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623495280378","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:56:47Z","timestamp":1787331407000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623495280378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,8]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,8]]}},"alternative-id":["10.1137\/S1052623495280378"],"URL":"https:\/\/doi.org\/10.1137\/s1052623495280378","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,8]]}}}