Please use this identifier to cite or link to this item: https://doi.org/10.1016/S0167-6377(01)00073-6
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dc.titleA further result on an implicit function theorem for locally Lipschitz functions
dc.contributor.authorSun, D.
dc.date.accessioned2014-10-28T02:28:07Z
dc.date.available2014-10-28T02:28:07Z
dc.date.issued2001-05
dc.identifier.citationSun, D. (2001-05). A further result on an implicit function theorem for locally Lipschitz functions. Operations Research Letters 28 (4) : 193-198. ScholarBank@NUS Repository. https://doi.org/10.1016/S0167-6377(01)00073-6
dc.identifier.issn01676377
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/102647
dc.description.abstractLet H:Rm × Rn → Rn be a locally Lipschitz function in a neighborhood of (ȳ,x̄) and H(ȳ,x̄) = 0 for some ȳ ∈ Rm and x̄ ∈ Rn. The implicit function theorem in the sense of Clarke (Pacific J. Math. 64 (1976) 97; Optimization and Nonsmooth Analysis, Wiley, New York, 1983) says that if πx∂H(ȳ,x̄) is of maximal rank, then there exist a neighborhood Y of ȳ and a Lipschitz function G(·):Y → Rn such that G(ȳ) = x̄ and for every y in Y, H(y,G(y)) = 0. In this paper, we shall further show that if H has a superlinear (quadratic) approximate property at (ȳ,x̄), then G has a superlinear (quadratic) approximate property at ȳ. This result is useful in designing Newton's methods for nonsmooth equations. © 2001 Elsevier Science B.V.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/S0167-6377(01)00073-6
dc.sourceScopus
dc.subjectHigher order approximation
dc.subjectImplicit function theorem
dc.subjectLocally Lipschitz function
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1016/S0167-6377(01)00073-6
dc.description.sourcetitleOperations Research Letters
dc.description.volume28
dc.description.issue4
dc.description.page193-198
dc.description.codenORLED
dc.identifier.isiut000173161000008
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