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Stochastic Approximation Method for Fixed Point Problems

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DOI: 10.4236/am.2012.312A293    3,225 Downloads   5,433 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Y. Alber, C. Chidume and J. Li, "Stochastic Approximation Method for Fixed Point Problems," Applied Mathematics, Vol. 3 No. 12A, 2012, pp. 2123-2132. doi: 10.4236/am.2012.312A293.

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