Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations

Authors:
Xiaojun Chen;Zuhair Nashed;Liqun Qi
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 17

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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 Rn 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.