{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T17:30:30Z","timestamp":1775151030679,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,10,30]],"date-time":"2013-10-30T00:00:00Z","timestamp":1383091200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2014,5]]},"DOI":"10.1007\/s10589-013-9615-y","type":"journal-article","created":{"date-parts":[[2013,10,29]],"date-time":"2013-10-29T16:20:06Z","timestamp":1383063606000},"page":"225-247","source":"Crossref","is-referenced-by-count":37,"title":["Local convergence of quasi-Newton methods under metric regularity"],"prefix":"10.1007","volume":"58","author":[{"given":"F. J.","family":"Arag\u00f3n Artacho","sequence":"first","affiliation":[]},{"given":"A.","family":"Belyakov","sequence":"additional","affiliation":[]},{"given":"A. L.","family":"Dontchev","sequence":"additional","affiliation":[]},{"given":"M.","family":"L\u00f3pez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,10,30]]},"reference":[{"key":"9615_CR1","doi-asserted-by":"crossref","DOI":"10.1201\/b12297","volume-title":"Numerical Methods for Equations and Its Applications","author":"I.K. Argyros","year":"2012","unstructured":"Argyros, I.K., Cho, Y.J., Hilout, S.: Numerical Methods for Equations and Its Applications. CRC Press, Boca Raton (2012)"},{"key":"9615_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"H.H. Bauschke","year":"2011","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, Berlin (2011)"},{"key":"9615_CR3","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s10898-010-9564-2","volume":"49","author":"B. Benahmed","year":"2011","unstructured":"Benahmed, B., Mokhtar-Kharroubi, H., Malafosse, B., Yassine, A.: Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations. J. Glob. Optim. 49, 365\u2013379 (2011)","journal-title":"J. Glob. Optim."},{"key":"9615_CR4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01204181","volume":"29","author":"J.F. Bonnans","year":"1994","unstructured":"Bonnans, J.F.: Local analysis of Newton-type methods for variational inequalities and nonlinear programming. Appl. Math. Optim. 29, 161\u2013186 (1994)","journal-title":"Appl. Math. Optim."},{"key":"9615_CR5","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1090\/S0025-5718-1974-0343581-1","volume":"28","author":"J.E. Dennis Jr.","year":"1974","unstructured":"Dennis, J.E. Jr., Mor\u00e9, J.J.: A characterization of superlinear convergence and its application to quasi-Newton methods. Math. Comput. 28, 549\u2013560 (1974)","journal-title":"Math. Comput."},{"key":"9615_CR6","first-page":"96","volume-title":"Recent Developments in Well-Posed Variational Problems","author":"A.L. Dontchev","year":"1995","unstructured":"Dontchev, A.L.: Characterizations of Lipschitz stability in optimization. In: Recent Developments in Well-Posed Variational Problems, pp. 96\u2013116. Kluwer Academic, Boston (1995)"},{"key":"9615_CR7","first-page":"327","volume":"322","author":"A.L. Dontchev","year":"1996","unstructured":"Dontchev, A.L.: Local convergence of the Newton method for generalized equation. C. R. Math. Acad. Sci. Paris, S\u00e9r. I 322, 327\u2013331 (1996)","journal-title":"C. R. Math. Acad. Sci. Paris, S\u00e9r. I"},{"key":"9615_CR8","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1137\/110833567","volume":"22","author":"A.L. Dontchev","year":"2012","unstructured":"Dontchev, A.L.: Generalizations of the Dennis\u2013Mor\u00e9 theorem. SIAM J. Optim. 22, 821\u2013830 (2012)","journal-title":"SIAM J. Optim."},{"key":"9615_CR9","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1090\/S0002-9939-1994-1215027-7","volume":"121","author":"A.L. Dontchev","year":"1994","unstructured":"Dontchev, A.L., Hager, W.W.: An inverse mapping theorem for set-valued maps. Proc. Am. Math. Soc. 121, 481\u2013489 (1994)","journal-title":"Proc. Am. Math. Soc."},{"key":"9615_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-87821-8","volume-title":"Implicit Functions and Solution Mappings. a View from Variational Analysis","author":"A.L. Dontchev","year":"2009","unstructured":"Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. a View from Variational Analysis. Springer, Dordrecht (2009)"},{"key":"9615_CR11","first-page":"975","volume":"19","author":"A.L. Dontchev","year":"2012","unstructured":"Dontchev, A.L., Rockafellar, R.T.: Parametric stability of solutions in models of economic equilibrium. J. Convex Anal. 19, 975\u2013997 (2012)","journal-title":"J. Convex Anal."},{"key":"9615_CR12","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1137\/0724045","volume":"24","author":"A. Griewank","year":"1987","unstructured":"Griewank, A.: The local convergence of Broyden-like methods on Lipschitzian problems in Hilbert spaces. SIAM J. Numer. Anal. 24, 684\u2013705 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"9615_CR13","doi-asserted-by":"crossref","unstructured":"Griewank, A.: Broyden updating, the good and the bad! Optimization stories. Doc. Math. 301\u2013315 (2012)","DOI":"10.4171\/dms\/6\/32"},{"key":"9615_CR14","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1137\/0722074","volume":"22","author":"S.M. Grzeg\u00f3rski","year":"1985","unstructured":"Grzeg\u00f3rski, S.M.: Orthogonal projections on convex sets for Newton-like methods. SIAM J. Numer. Anal. 22, 1208\u20131219 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"9615_CR15","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1137\/0802025","volume":"2","author":"D.M. Hwang","year":"1992","unstructured":"Hwang, D.M., Kelley, C.T.: Convergence of Broyden\u2019s method in Banach spaces. SIAM J. Optim. 2, 505\u2013532 (1992)","journal-title":"SIAM J. Optim."},{"key":"9615_CR16","unstructured":"Josephy, N.H.: Newton\u2019s method for generalized equations and the PIES energy model. Ph.D. Dissertation, Department of Industrial Engineering, University of Wisconsin-Madison (1979)"},{"key":"9615_CR17","series-title":"Frontiers in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative Methods for Linear and Nonlinear Equations","author":"C.T. Kelley","year":"1995","unstructured":"Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. Frontiers in Applied Mathematics, vol. 16. SIAM, Philadelphia (1995). With separately available software"},{"key":"9615_CR18","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1137\/0801011","volume":"1","author":"C.T. Kelley","year":"1991","unstructured":"Kelley, C.T., Sachs, E.: A new proof of superlinear convergence for Broyden\u2019s method in Hilbert space. SIAM J. Optim. 1, 146\u2013150 (1991)","journal-title":"SIAM J. Optim."},{"key":"9615_CR19","volume-title":"Nonsmooth Equations in Optimization","author":"D. Klatte","year":"2002","unstructured":"Klatte, D., Kummer, B.: Nonsmooth Equations in Optimization. Kluwer Academic, Boston (2002)"},{"key":"9615_CR20","volume-title":"Introduction to Functional Analysis","author":"R. Meise","year":"2004","unstructured":"Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, London (2004)"},{"key":"9615_CR21","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1287\/moor.5.1.43","volume":"5","author":"S.M. Robinson","year":"1980","unstructured":"Robinson, S.M.: Strongly regular generalized equations. Math. Oper. Res. 5, 43\u201362 (1980)","journal-title":"Math. Oper. Res."},{"key":"9615_CR22","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1137\/0323026","volume":"23","author":"E.W. Sachs","year":"1985","unstructured":"Sachs, E.W.: Convergence rates of quasi-Newton algorithms for some nonsmooth optimization problems. SIAM J. Control Optim. 23, 401\u2013418 (1985)","journal-title":"SIAM J. Control Optim."},{"key":"9615_CR23","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF01589442","volume":"35","author":"E.W. Sachs","year":"1986","unstructured":"Sachs, E.W.: Broyden\u2019s method in Hilbert space. Math. Program. 35, 71\u201382 (1986)","journal-title":"Math. Program."},{"key":"9615_CR24","series-title":"Springer Optimization and Its Applications","volume-title":"Optimization Theory and Methods: Nonlinear Programming","author":"W. Sun","year":"2006","unstructured":"Sun, W., Yuan, Y.-X.: Optimization Theory and Methods: Nonlinear Programming. Springer Optimization and Its Applications, vol. 1. Springer, New York (2006)"},{"key":"9615_CR25","first-page":"305","volume":"16","author":"Y. Wen-huan","year":"1998","unstructured":"Wen-huan, Y.: A quasi-Newton method in infinite-dimensional spaces and its application for solving a parabolic inverse problem. J. Comput. Math. 16, 305\u2013318 (1998)","journal-title":"J. Comput. Math."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9615-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-013-9615-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9615-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T19:04:35Z","timestamp":1688583875000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-013-9615-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,30]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["9615"],"URL":"https:\/\/doi.org\/10.1007\/s10589-013-9615-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,30]]}}}