{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T04:05:15Z","timestamp":1649131515756},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2010,1,23]],"date-time":"2010-01-23T00:00:00Z","timestamp":1264204800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2010,12]]},"DOI":"10.1007\/s11075-010-9364-2","type":"journal-article","created":{"date-parts":[[2010,1,22]],"date-time":"2010-01-22T10:42:28Z","timestamp":1264156948000},"page":"447-466","source":"Crossref","is-referenced-by-count":2,"title":["A Kantorovich-type convergence analysis of the Newton\u2013Josephy method for solving variational inequalities"],"prefix":"10.1007","volume":"55","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sa\u00efd","family":"Hilout","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,1,23]]},"reference":[{"key":"9364_CR1","volume-title":"Introduction to Interval Computations. Translated from the German by Jon Rokne, Computer Science and Applied Mathematics","author":"G Alefeld","year":"1983","unstructured":"Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Translated from the German by Jon Rokne, Computer Science and Applied Mathematics. Academic, New York (1983)"},{"key":"9364_CR2","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.cam.2004.01.029","volume":"169","author":"IK Argyros","year":"2004","unstructured":"Argyros, I.K.: On the Newton\u2013Kantorovich hypothesis for solving equations. J. Comput. Appl. Math. 169, 315\u2013332 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"9364_CR3","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.jmaa.2004.04.008","volume":"298","author":"IK Argyros","year":"2004","unstructured":"Argyros, I.K.: A unifying local\u2013semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl. 298, 374\u2013397 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"9364_CR4","volume-title":"Convergence and Applications of Newton-Type Iterations","author":"IK Argyros","year":"2008","unstructured":"Argyros, I.K.: Convergence and Applications of Newton-Type Iterations. Springer, New York (2008)"},{"key":"9364_CR5","volume-title":"Efficient Methods for Solving Equations and Variational Inequalities","author":"IK Argyros","year":"2009","unstructured":"Argyros, I.K., Hilout, S.: Efficient Methods for Solving Equations and Variational Inequalities. Polimetrica, Milan (2009)"},{"key":"9364_CR6","first-page":"119","volume":"4","author":"IK Argyros","year":"2009","unstructured":"Argyros, I.K., Hilout, S.: Enclosing roots of polynomial equations and their applications to iterative processes. Surveys Math. Appl. 4, 119\u2013132 (2009)","journal-title":"Surveys Math. Appl."},{"key":"9364_CR7","unstructured":"Br\u00e9zis, H.: Op\u00e9rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, No. 5, Notas de Matem\u00e1tica (50). North-Holland, Amsterdam (1973)"},{"key":"9364_CR8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01585559","volume":"69","author":"B Chen","year":"1995","unstructured":"Chen, B., Harker, P.T.: A continuation method for monotone variational inequalities. Math. Program. 69, 273\u2013253 (1995)","journal-title":"Math. Program."},{"key":"9364_CR9","unstructured":"Eaves, B.C.: A Locally Quadratically Convergent Algorithm for Computing Stationary Point. Dpt of Operations Research, Stanford University, Palo Alto (1978)"},{"key":"9364_CR10","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","volume":"48","author":"PT Harker","year":"1990","unstructured":"Harker, P.T., Pang, J.S.: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program. Ser. B, 48, 161\u2013220 (1990)","journal-title":"Math. Program. Ser. B"},{"key":"9364_CR11","doi-asserted-by":"crossref","unstructured":"Izmailov, A.F, Solodov, M.V.: Inexact Josephy\u2013Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization. Comput. Optim. Appl. doi: 10.1007\/s10589-009-9265-2","DOI":"10.1007\/s10589-009-9265-2"},{"key":"9364_CR12","unstructured":"Josephy, N.H.: Newton\u2019s method for generalized equations, Technical report no. 1965, Mathematics Research Center, University of Wisconsin, Madison, WI (1979)"},{"key":"9364_CR13","volume-title":"Functional Analysis","author":"LV Kantorovich","year":"1982","unstructured":"Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Pergamon, Oxford (1982)"},{"key":"9364_CR14","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"LM Ortega","year":"1970","unstructured":"Ortega, L.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic, New York (1970)"},{"key":"9364_CR15","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1080\/10556789908805734","volume":"10","author":"Ji-M Peng","year":"1999","unstructured":"Peng, Ji-M., Kanzow, C., Fukushima, M.: A hybrid Josephy\u2013Newton method for solving box constrained variational inequality problems via the D-gap function. Optim. Methods Softw. 10, 687\u2013710 (1999)","journal-title":"Optim. Methods Softw."},{"key":"9364_CR16","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/BFb0120850","volume":"10","author":"SM Robinson","year":"1979","unstructured":"Robinson, S.M.: Generalized equations and their solutions, part I: Basic theory. Math. Program. Stud. 10, 128\u2013141 (1979)","journal-title":"Math. Program. Stud."},{"key":"9364_CR17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1287\/moor.5.1.43","volume":"5","author":"SM Robinson","year":"1980","unstructured":"Robinson, S.M.: Strongly regular generalized equations. Math. Oper. Res. 5, 43\u201362 (1980)","journal-title":"Math. Oper. Res."},{"key":"9364_CR18","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1080\/1055678021000056563","volume":"17","author":"MV Solodov","year":"2002","unstructured":"Solodov, M.V., Svaiter, B.F.: A new proximal-based globalization strategy for the Josephy\u2013Newton method for variational inequalities. Optim. Methods Softw. 17, 965\u2013983 (2002)","journal-title":"Optim. Methods Softw."},{"key":"9364_CR19","unstructured":"Wang, Z.Y.: Semilocal convergence of Newton\u2019s method for finite-dimensional variational inequalities and nonlinear complementarity problems, Dissertation, Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Karlsruhe (2005)"},{"key":"9364_CR20","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/zamm.200700072","volume":"88","author":"ZY Wang","year":"2008","unstructured":"Wang, Z.Y.: Extensions of Kantorovich theorem to variational inequality problems. Z. Angew. Math. Mech. 88, 179\u2013190 (2008)","journal-title":"Z. Angew. Math. Mech."},{"key":"9364_CR21","unstructured":"Wang, Z.Y.: Extensions of the Newton\u2013Kantorovich theorem to variational inequality problems. http:\/\/math.nju.edu.cn\/~zywang\/paper\/Kantorovich_VIP.pdf (2009)"},{"key":"9364_CR22","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1007\/BF02438285","volume":"25","author":"ZY Wang","year":"2004","unstructured":"Wang, Z.Y., Shen, Z.H.: Kantorovich theorem for variational inequalities, (English Ed.). Appl. Math. Mech. 25, 1291\u20131297 (2004)","journal-title":"Appl. Math. Mech."},{"key":"9364_CR23","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF01581695","volume":"65","author":"B Xiao","year":"1994","unstructured":"Xiao, B., Harker, P.T.: A nonsmooth Newton method for variational inequality. I: Theory, Math. Program. 65, 151\u2013194 (1994)","journal-title":"Theory, Math. Program."},{"key":"9364_CR24","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF01581696","volume":"65","author":"B Xiao","year":"1994","unstructured":"Xiao, B., Harker, P.T.: A nonsmooth Newton method for variational inequality, II: numerical results. Math. Program. 65, 195\u2013216 (1994)","journal-title":"Math. Program."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-010-9364-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-010-9364-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-010-9364-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:14Z","timestamp":1559365694000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-010-9364-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,23]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["9364"],"URL":"https:\/\/doi.org\/10.1007\/s11075-010-9364-2","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1,23]]}}}