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http://hdl.handle.net/10397/6031
Title: | Smoothing methods and semismooth methods for nondifferentiable operator equations | Authors: | Chen, X Nashed, Z Qi, L |
Issue Date: | 2000 | Source: | SIAM journal on numerical analysis, 2000, v. 38, no. 4, p. 1200-1216 | 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. | Keywords: | Smoothing methods Semismooth methods Superlinear convergence Nondifferentiable operator equation Nonsmooth elliptic partial differential equations |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM Journal on numerical analysis | 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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Chen_Smoothing_Methods_Semismooth.pdf | 189.98 kB | Adobe PDF | View/Open |
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