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Title: An Iterative Procedure for Solving Nonsmooth Generalized Equation
Authors: Marinov, Rumen Tsanev
Keywords: Set-Valued Maps
Generalized Equation
Linear Convergence
Aubin Continuity
Issue Date: 2008
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 34, No 2, (2008), 441p-454p
Abstract: In this article, we study a general iterative procedure of the following form 0 ∈ f(xk)+F(xk+1), where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations in the nonsmooth framework. We prove that this method is locally Q-linearly convergent to x* a solution of the generalized equation 0 ∈ f(x)+F(x) if the set-valued map [f(x*)+g(·)−g(x*)+F(·)]−1 is Aubin continuous at (0,x*), where g:X→ Y is a function, whose Fréchet derivative is L-Lipschitz.
Description: 2000 Mathematics Subject Classification: 47H04, 65K10.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 2

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