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.
