{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:50:46Z","timestamp":1759837846740},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1994,2,1]],"date-time":"1994-02-01T00:00:00Z","timestamp":760060800000},"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":[[1994,2]]},"DOI":"10.1007\/bf01581695","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T09:42:27Z","timestamp":1114681347000},"page":"151-194","source":"Crossref","is-referenced-by-count":40,"title":["A nonsmooth Newton method for variational inequalities, I: Theory"],"prefix":"10.1007","volume":"65","author":[{"given":"Baichun","family":"Xiao","sequence":"first","affiliation":[]},{"given":"Patrick T.","family":"Harker","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","unstructured":"M.S. Bazaraa and C.M. Shetty,Nonlinear Programming: Theory and Algorithms (John Wiley & Sons, 1979)."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/BF01589441","volume":"35","author":"M. Fukushima","year":"1986","unstructured":"M. Fukushima, \u201cA relaxed projection method for variational inequalities,\u201dMathematical Programming 35 (1986) 58\u201370.","journal-title":"Mathematical Programming"},{"key":"CR3","volume-title":"\u201cEquivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems,\u201d Technical Report 89007","author":"M. Fukushima","year":"1989","unstructured":"M. Fukushima, \u201cEquivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems,\u201d Technical Report 89007, Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University (Kyoto, Japan, 1989)."},{"key":"CR4","volume-title":"Pathways to Solutions, Fixed Points and Equilibria","author":"C.B. Garcia","year":"1981","unstructured":"C.B. Garcia and W.I. Zangwill,Pathways to Solutions, Fixed Points and Equilibria (Prentice-Hall, Englewood Cliffs, NJ, 1981)."},{"key":"CR5","first-page":"265","volume":"26","author":"P.T. Harker","year":"1990","unstructured":"P.T. Harker and J.S. Pang, \u201cA damped-Newton method for the linear complementarity problem,\u201d in: G. Allgower and K. Georg, ed.,AMS Transactions on Applied Mathematics 26 (1990) 265\u2013284.","journal-title":"AMS Transactions on Applied Mathematics"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01582249","volume":"48","author":"P.T. Harker","year":"1990","unstructured":"P.T. Harker and J.S. Pang, \u201cFinite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications,\u201dMathematical Programming B 48 (1990) 1\u201360.","journal-title":"Mathematical Programming B"},{"key":"CR7","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 48 (1990) 339\u2013357.","journal-title":"Mathematical Programming"},{"key":"CR8","volume-title":"\u201cNewton's method for generalized equations,\u201d Technical Report No. 1965","author":"N.H. Josephy","year":"1979","unstructured":"N.H. Josephy, \u201cNewton's method for generalized equations,\u201d Technical Report No. 1965, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979)."},{"key":"CR9","volume-title":"\u201cQuasi-Newton methods for generalized equations,\u201d Technical Report No. 1966","author":"N.H. Josephy","year":"1979","unstructured":"N.H. Josephy, \u201cQuasi-Newton methods for generalized equations,\u201d Technical Report No. 1966, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979)."},{"key":"CR10","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 ofPC 1 equations,\u201dJournal of Operations Research Society of Japan 29 (1986) 352\u2013374.","journal-title":"Journal of Operations Research Society of Japan"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0191-2615(84)90026-2","volume":"18B","author":"S. Lawphongpanich","year":"1984","unstructured":"S. Lawphongpanich and D.W. Hearn, \u201cSimplicial decomposition of asymmetric traffic assignment problem,\u201dTransportation Research 18B (1984) 123\u2013133.","journal-title":"Transportation Research"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0167-6377(87)90007-1","volume":"6","author":"P. Marcotte","year":"1987","unstructured":"P. Marcotte and J.P. Dussault, \u201cA note on a globally convergent Newton method for solving monotone variational inequalities,\u201dOperations Research Letters 6 (1987) 35\u201342.","journal-title":"Operations Research Letters"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"273","DOI":"10.24033\/bsmf.1625","volume":"93","author":"J.J. Moreau","year":"1965","unstructured":"J.J. Moreau, \u201cProximit\u00e9 et dualit\u00e9 dans un espace Hilberiten,\u201dBulletin of the Society of Mathematics of France 93 (1965) 273\u2013299.","journal-title":"Bulletin of the Society of Mathematics of France"},{"key":"CR14","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1007\/BF02591989","volume":"36","author":"J.S. Pang","year":"1986","unstructured":"J.S. Pang, \u201cInexact Newton methods for the nonlinear complementarity problem,\u201dMathematical Programming 36 (1986) 54\u201371.","journal-title":"Mathematical Programming"},{"key":"CR15","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":"CR16","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1007\/BF01585112","volume":"24","author":"J.S. Pang","year":"1982","unstructured":"J.S. Pang and D. Chan, \u201cIterative methods for variational and complementarity problems,\u201dMathematical Programming 24 (1982) 284\u2013313.","journal-title":"Mathematical Programming"},{"key":"CR17","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":"CR18","volume-title":"\u201cImplicit B-differentiability in generalized equations,\u201d Technical Summary Report No. 2854","author":"S.M. Robinson","year":"1985","unstructured":"S.M. Robinson, \u201cImplicit B-differentiability in generalized equations,\u201d Technical Summary Report No. 2854, Mathematics Research Center, University of Wisconsin (Madison, WI, 1985)."},{"key":"CR19","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":"CR20","volume-title":"An implicit-function theorem for B-differentiable functions","author":"S.M. Robinson","year":"1988","unstructured":"S.M. Robinson, \u201cAn implicit-function theorem for B-differentiable functions,\u201d Manuscript, Department of Industrial Engineering, University of Wisconsin (Madison, WI, 1988)."},{"key":"CR21","volume-title":"Newton's method for a class of nonsmooth functions","author":"S.M. Robinson","year":"1989","unstructured":"S.M. Robinson, \u201cNewton's method for a class of nonsmooth functions,\u201d Manuscript, Department of Industrial Engineering, University of Wisconsin (Madison, WI, 1989)."},{"key":"CR22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.2140\/pjm.1970.33.209","volume":"33","author":"R.T. Rockafellar","year":"1970","unstructured":"R.T. Rockafellar, \u201cOn the maximal monotonicity of subdifferential mappings,\u201dPacific Journal of Mathematics 33 (1970) 209\u2013216.","journal-title":"Pacific Journal of Mathematics"},{"key":"CR23","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"R.T. Rockafellar","year":"1976","unstructured":"R.T. Rockafellar, \u201cMonotone operators and the proximal point algorithm,\u201dSIAM Journal on Control and Optimization 14 (1976) 877\u2013898.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"CR24","volume-title":"\u201cOn concepts of directional differentiability,\u201d Research Report 73\/88(18)","author":"A. Shapiro","year":"1988","unstructured":"A. Shapiro, \u201cOn concepts of directional differentiability,\u201d Research Report 73\/88(18), Department of Mathematics and Applied Mathematics, University of South Africa (Pretoria, South Africa, 1988)."},{"key":"CR25","volume-title":"\u201cA note on least two norm solutions of monotone complementarity problems,\u201d Technical Summary Report No. 2844","author":"P.K. Subramanian","year":"1985","unstructured":"P.K. Subramanian, \u201cA note on least two norm solutions of monotone complementarity problems,\u201d Technical Summary Report No. 2844, Mathematics Research Center, University of Wisconsin (Madison, WI, 1985)."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01581695.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01581695\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01581695","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:12:20Z","timestamp":1556896340000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01581695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,2]]},"references-count":25,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1994,2]]}},"alternative-id":["BF01581695"],"URL":"https:\/\/doi.org\/10.1007\/bf01581695","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,2]]}}}