{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:25:55Z","timestamp":1761611155173},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1992,8,1]],"date-time":"1992-08-01T00:00:00Z","timestamp":712627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1992,8]]},"DOI":"10.1007\/bf01580895","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T08:58:11Z","timestamp":1114678691000},"page":"71-89","source":"Crossref","is-referenced-by-count":51,"title":["Local convergence of quasi-Newton methods for B-differentiable equations"],"prefix":"10.1007","volume":"56","author":[{"given":"Chi-Ming","family":"Ip","sequence":"first","affiliation":[]},{"given":"Jerzy","family":"Kyparisis","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1090\/S0025-5718-1965-0198670-6","volume":"19","author":"C.G. Broyden","year":"1965","unstructured":"C.G. Broyden, \u201cA class of methods for solving nonlinear simultaneous equations,\u201dMathematics of Computation 19 (1965) 577\u2013593.","journal-title":"Mathematics of Computation"},{"key":"CR2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1093\/imamat\/12.3.223","volume":"12","author":"C.G. Broyden","year":"1973","unstructured":"C.G. Broyden, J.E. Dennis Jr. and J.J. Mor\u00e9, \u201cOn the local and superlinear convergence of quasi-Newton methods,\u201dJournal of the Institute of Mathematics and its Applications 12 (1973) 223\u2013245.","journal-title":"Journal of the Institute of Mathematics and its Applications"},{"key":"CR3","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":"J.E. Dennis Jr. and J.J. Mor\u00e9, \u201cA characterization of superlinear convergence and its application to quasi-Newton methods,\u201dMathematics of Computation 28 (1974) 549\u2013560.","journal-title":"Mathematics of Computation"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1137\/1019005","volume":"19","author":"J.E. Dennis Jr.","year":"1977","unstructured":"J.E. Dennis Jr. and J.J. Mor\u00e9, \u201cQuasi-Newton methods, motivation and theory,\u201dSIAM Review 19 (1977) 46\u201389.","journal-title":"SIAM Review"},{"key":"CR5","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"J.E. Dennis Jr.","year":"1983","unstructured":"J.E. Dennis Jr. and R.B. Schnabel,Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983)."},{"key":"CR6","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1137\/0718067","volume":"18","author":"J.E. Dennis Jr.","year":"1981","unstructured":"J.E. Dennis Jr. and H.F. Walker, \u201cConvergence theorems for least-change secant update methods,\u201dSIAM Journal on Numerical Analysis 18 (1981) 949\u2013987.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","volume":"48","author":"P.T. Harker","year":"1990","unstructured":"P.T. Harker and J.S. Pang, \u201cFinite-dimensional variational inequality and non-linear complementarity problems: A survey of theory, algorithms and applications,\u201dMathematical Programming (Series B) 48 (1990) 161\u2013220.","journal-title":"Mathematical Programming (Series B)"},{"key":"CR8","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF01582262","volume":"48","author":"P.T. Harker","year":"1990","unstructured":"P.T. Harker and B. Xiao, \u201cNewton's method for the nonlinear complementarity problem: A B-differentiable equation approach,\u201dMathematical Programming (Series B) 48 (1990) 339\u2013357.","journal-title":"Mathematical Programming (Series B)"},{"key":"CR9","volume-title":"\u201cNewton's method for generalized equations,\u201d Technical Summary Report No. 1965","author":"N.H. Josephy","year":"1979","unstructured":"N.H. Josephy, \u201cNewton's method for generalized equations,\u201d Technical Summary Report No. 1965, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979)."},{"key":"CR10","volume-title":"\u201cQuasi-Newton methods for generalized equations,\u201d Technical Summary Report No. 1966","author":"N.H. Josephy","year":"1979","unstructured":"N.H. Josephy, \u201cQuasi-Newton methods for generalized equations,\u201d Technical Summary Report No. 1966, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979)."},{"key":"CR11","doi-asserted-by":"crossref","first-page":"352","DOI":"10.15807\/jorsj.29.352","volume":"29","author":"M. Kojima","year":"1986","unstructured":"M. Kojima and S. Shindo, \u201cExtensions of Newton and quasi-Newton methods to systems of PC1 equations,\u201dJournal of Operations Research Society of Japan 29 (1986) 352\u2013374.","journal-title":"Journal of Operations Research Society of Japan"},{"key":"CR12","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"J.M. Ortega","year":"1970","unstructured":"J.M. Ortega and W.C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970)."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1287\/moor.15.2.311","volume":"15","author":"J.S. Pang","year":"1990","unstructured":"J.S. Pang, \u201cNewton's method for B-differentiable equations,\u201dMathematics of Operations Research 15 (1990) 311\u2013341.","journal-title":"Mathematics of Operations Research"},{"key":"CR14","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF01586928","volume":"51","author":"J.S. Pang","year":"1991","unstructured":"J.S. Pang, \u201cA B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems,\u201dMathematical Programming 51 (1991) 101\u2013131.","journal-title":"Mathematical Programming"},{"key":"CR15","volume-title":"\u201cA nonsmooth version of Newton's method and an interior point algorithm for convex programming,\u201d Technical Report 90-01","author":"L. Qi","year":"1990","unstructured":"L. Qi and J. Sun, \u201cA nonsmooth version of Newton's method and an interior point algorithm for convex programming,\u201d Technical Report 90-01, Department of Industrial Engineering and Management Sciences, Northwestern University (Evanston, IL, 1990)."},{"key":"CR16","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/BFb0121154","volume":"30","author":"S.M. Robinson","year":"1987","unstructured":"S.M. Robinson, \u201cLocal structure of feasible sets in nonlinear programming, part III: stability and sensitivity,\u201dMathematical Programming Study 30 (1987) 45\u201366.","journal-title":"Mathematical Programming Study"},{"key":"CR17","series-title":"Working paper","volume-title":"Newton's method for a class of nonsmooth functions","author":"S.M. Robinson","year":"1988","unstructured":"S.M. Robinson, \u201cNewton's method for a class of nonsmooth functions,\u201d Working paper, Department of Industrial Engineering, University of Wisconsin (Madison, WI, 1988)."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580895.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01580895\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580895","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:12:12Z","timestamp":1556896332000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01580895"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,8]]},"references-count":17,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1992,8]]}},"alternative-id":["BF01580895"],"URL":"https:\/\/doi.org\/10.1007\/bf01580895","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,8]]}}}