Title

Stochastic Approximation Method for Fixed Point Problems

Document Type

Article

Publication Date

12-2012

Original Publication Title

Applied Mathematics

Department

Mathematical Sciences

DOI

10.4236/am.2012.312A293

Abstract

We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.

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