{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:46:59Z","timestamp":1774626419412,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,1,26]],"date-time":"2017-01-26T00:00:00Z","timestamp":1485388800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11171221"],"award-info":[{"award-number":["11171221"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai","doi-asserted-by":"publisher","award":["14ZR142920"],"award-info":[{"award-number":["14ZR142920"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation Program of Shanghai Municipal Education Commission","award":["15ZZ073"],"award-info":[{"award-number":["15ZZ073"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s11075-017-0267-3","type":"journal-article","created":{"date-parts":[[2017,1,25]],"date-time":"2017-01-25T23:20:55Z","timestamp":1485386455000},"page":"473-485","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A nonsmooth Levenberg-Marquardt method for vertical complementarity problems"],"prefix":"10.1007","volume":"76","author":[{"given":"Linsen","family":"Song","sequence":"first","affiliation":[]},{"given":"Yan","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,1,26]]},"reference":[{"issue":"1","key":"267_CR1","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1287\/moor.18.1.227","volume":"18","author":"LQ Qi","year":"1993","unstructured":"Qi, L.Q.: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper Res. 18(1), 227\u2013244 (1993)","journal-title":"Math. Oper Res."},{"issue":"1","key":"267_CR2","first-page":"353","volume":"58","author":"LQ Qi","year":"1993","unstructured":"Qi, L.Q., Sun, J.: A nonsmooth version of Newton\u2019s method. Math. Program. 58(1), 353\u2013367 (1993)","journal-title":"Math. Program."},{"issue":"2","key":"267_CR3","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1137\/S1052623494274970","volume":"7","author":"DF Sun","year":"1997","unstructured":"Sun, D.F., Han, J.Y.: Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM J. Optim. 7(2), 463\u2013480 (1997)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"267_CR4","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/BF02614395","volume":"76","author":"F Facchinei","year":"1997","unstructured":"Facchinei, F., Kanzow, C.: A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Math. Program. 76(3), 493\u2013512 (1997)","journal-title":"Math. Program."},{"key":"267_CR5","first-page":"239","volume":"15","author":"N Yamashita","year":"2001","unstructured":"Yamashita, N., Fukushima, M.: On the rate of convergence of the Levenberg-Marquardt method. Computing 15, 239\u2013249 (2001)","journal-title":"Computing"},{"issue":"1","key":"267_CR6","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s00607-004-0083-1","volume":"74","author":"J Fan","year":"2005","unstructured":"Fan, J., Yuan, Y.X.: On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption. Computing 74(1), 23\u201339 (2005)","journal-title":"Computing"},{"issue":"1","key":"267_CR7","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s10589-005-3074-z","volume":"34","author":"J Fan","year":"2006","unstructured":"Fan, J., Pan, J.: Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition. Comput. Optim. Appl. 34(1), 47\u201362 (2006)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"267_CR8","first-page":"625","volume":"21","author":"JY Fan","year":"2003","unstructured":"Fan, J.Y.: A modified Levenberg-Marquardt algorithm for singular system of nonlinear equations. J. Comput. Math. 21(5), 625\u2013636 (2003)","journal-title":"J. Comput. Math."},{"issue":"4","key":"267_CR9","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s11075-010-9439-0","volume":"57","author":"R Andreani","year":"2007","unstructured":"Andreani, R., J\u00fadice, J., Mart\u00ednez, J.M., Patricio, J.: A projected-gradient interior-point algorithm for complementarity problems. Numer. Algorithm 57(4), 457\u2013485 (2007)","journal-title":"Numer. Algorithm"},{"issue":"277","key":"267_CR10","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1090\/S0025-5718-2011-02496-8","volume":"81","author":"J Fan","year":"2012","unstructured":"Fan, J.: The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence. Math. Comput. 81(277), 447\u2013466 (2012)","journal-title":"Math. Comput."},{"issue":"2","key":"267_CR11","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s10589-010-9349-z","volume":"50","author":"SH Xiang","year":"2011","unstructured":"Xiang, S.H., Chen, X.J.: Computation of generalized differentials in nonlinear complementarity problems. Comput. Optim. Appl. 50(2), 403\u2013423 (2011)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"267_CR12","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1081\/NFA-100105308","volume":"22","author":"Y Gao","year":"2001","unstructured":"Gao, Y.: Calculating an element of B-differential for a vector-valued maximum function. Numer. Funct. Anal. Optim. 22(5), 561\u2013575 (2001)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"2","key":"267_CR13","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1016\/j.na.2009.07.040","volume":"72","author":"ZD Huang","year":"2010","unstructured":"Huang, Z.D., Ma, G.C.: On the computation of an element of Clarke generalized Jacobian for a vector-valued max function. Nonlinear Anal. 72(2), 998\u20131009 (2010)","journal-title":"Nonlinear Anal."},{"key":"267_CR14","volume-title":"Nonsmooth optimization","author":"Y Gao","year":"2008","unstructured":"Gao, Y.: Nonsmooth optimization. Science Press, Beijing (2008)"},{"key":"267_CR15","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.cam.2015.04.040","volume":"288","author":"A Keyvan","year":"2015","unstructured":"Keyvan, A., Faramarz, R.: A modified two steps Levenberg-Marquardt method for nonlinear equations. J. Comput. Appl. Math. 288, 341\u2013350 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"267_CR16","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1287\/moor.21.2.401","volume":"21","author":"JS Pang","year":"1996","unstructured":"Pang, J.S., Ralph, D.: Piecewise smoothness, local invertibility, and parametric analysis of normal maps. Math. Oper. Res. 21, 401\u2013426 (1996)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"267_CR17","doi-asserted-by":"crossref","first-page":"317","DOI":"10.4208\/jcm.1512-m2015-0333","volume":"34","author":"LY Qi","year":"2016","unstructured":"Qi, L.Y., Xiao, X.T., Zhang, L.W.: A parameter-self-adjusting Levenberg-Marquardt method for solving nonsmooth equations. J. Comput. Math. 34(3), 317\u2013338 (2016)","journal-title":"J. Comput. Math."},{"key":"267_CR18","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/s101070050104","volume":"86","author":"JM Peng","year":"1999","unstructured":"Peng, J.M., Lin, Z.H.: A non-interior continuation method for generalized linear complementarity problem. Math. Program. 86, 533\u2013563 (1999)","journal-title":"Math. Program."},{"issue":"5","key":"267_CR19","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s10492-011-0027-y","volume":"56","author":"SQ Du","year":"2011","unstructured":"Du, S.Q., Gao, Y.: Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations. Appl. Math. 56(5), 481\u2013498 (2011)","journal-title":"Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0267-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0267-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0267-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,9,21]],"date-time":"2017-09-21T07:32:25Z","timestamp":1505979145000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0267-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,26]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["267"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0267-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,26]]}}}