{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:40Z","timestamp":1787329300341,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>The dogleg method is a classical trust-region technique for globalizing Newton's method. While it is widely used in optimization, including large-scale optimization via truncated-Newton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexact Newton context and provide a global convergence analysis for it. We then discuss certain issues that may arise with the standard dogleg implementational strategy and propose modified strategies that address them. Newton\u2013Krylov methods have provided important motivation for this work, and we conclude with a report on numerical experiments involving a Newton\u2013GMRES dogleg method applied to benchmark CFD problems.<\/jats:p>","DOI":"10.1137\/050632166","type":"journal-article","created":{"date-parts":[[2008,5,4]],"date-time":"2008-05-04T04:04:04Z","timestamp":1209873844000},"page":"2112-2132","source":"Crossref","is-referenced-by-count":21,"title":["Inexact Newton Dogleg Methods"],"prefix":"10.1137","volume":"46","author":[{"given":"Roger P.","family":"Pawlowski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph P.","family":"Simonis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Homer F.","family":"Walker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John N.","family":"Shadid","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,5,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"K. 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