Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6031
Title: Smoothing methods and semismooth methods for nondifferentiable operator equations
Authors: Chen, X 
Nashed, Z
Qi, L 
Keywords: Smoothing methods
Semismooth methods
Superlinear convergence
Nondifferentiable operator equation
Nonsmooth elliptic partial differential equations
Issue Date: 2000
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on numerical analysis, 2000, v. 38, no. 4, p. 1200-1216 How to cite?
Journal: SIAM Journal on numerical analysis 
Abstract: We consider superlinearly convergent analogues of Newton methods for nondifferentiable operator equations in function spaces. The superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally Lipschitzian operator in R[sup n] is based on Rademacher's theorem which does not hold in function spaces. We introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework. We show that a function is slantly differentiable at a point if and only if it is Lipschitz continuous at that point. An application to the Dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed.
URI: http://hdl.handle.net/10397/6031
ISSN: 0036-1429 (print)
1095-7170 (online)
DOI: 10.1137/S0036142999356719
Rights: ©2000 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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