Please use this identifier to cite or link to this item: https://doi.org/10.1016/S0167-6377(01)00073-6
Title: A further result on an implicit function theorem for locally Lipschitz functions
Authors: Sun, D. 
Keywords: Higher order approximation
Implicit function theorem
Locally Lipschitz function
Issue Date: May-2001
Citation: Sun, 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
Abstract: Let 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.
Source Title: Operations Research Letters
URI: http://scholarbank.nus.edu.sg/handle/10635/102647
ISSN: 01676377
DOI: 10.1016/S0167-6377(01)00073-6
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

31
checked on Oct 16, 2018

WEB OF SCIENCETM
Citations

30
checked on Oct 16, 2018

Page view(s)

71
checked on Oct 12, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.