# An Iterative Procedure for Solving Nonsmooth Generalized Equation

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 2, page 441-454
- ISSN: 1310-6600

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topMarinov, Rumen Tsanev. "An Iterative Procedure for Solving Nonsmooth Generalized Equation." Serdica Mathematical Journal 34.2 (2008): 441-454. <http://eudml.org/doc/281452>.

@article{Marinov2008,

abstract = {2000 Mathematics Subject Classification: 47H04, 65K10.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.},

author = {Marinov, Rumen Tsanev},

journal = {Serdica Mathematical Journal},

keywords = {Set-Valued Maps; Generalized Equation; Linear Convergence; Aubin Continuity; set-valued maps; generalized equation; linear convergence; Aubin continuity; Banach space; normed space},

language = {eng},

number = {2},

pages = {441-454},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {An Iterative Procedure for Solving Nonsmooth Generalized Equation},

url = {http://eudml.org/doc/281452},

volume = {34},

year = {2008},

}

TY - JOUR

AU - Marinov, Rumen Tsanev

TI - An Iterative Procedure for Solving Nonsmooth Generalized Equation

JO - Serdica Mathematical Journal

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 34

IS - 2

SP - 441

EP - 454

AB - 2000 Mathematics Subject Classification: 47H04, 65K10.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.

LA - eng

KW - Set-Valued Maps; Generalized Equation; Linear Convergence; Aubin Continuity; set-valued maps; generalized equation; linear convergence; Aubin continuity; Banach space; normed space

UR - http://eudml.org/doc/281452

ER -

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