Geodesic
An Iterative Procedure for Solving Nonsmooth Generalized Equation
Serdica Mathematical Journal, Tome 34 (2008) no. 2, pp. 441-454

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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.
Keywords: Set-Valued Maps, Generalized Equation, Linear Convergence, Aubin Continuity 
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     author = {Marinov, Rumen Tsanev},
     title = {An {Iterative} {Procedure} for {Solving} {Nonsmooth} {Generalized} {Equation}},
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     url = {http://geodesic.mathdoc.fr/item/SMJ2_2008_34_2_a4/}
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Marinov, Rumen Tsanev. An Iterative Procedure for Solving Nonsmooth Generalized Equation. Serdica Mathematical Journal, Tome 34 (2008) no. 2, pp. 441-454. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_2_a4/