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Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity

Borwein, Jonathan M. and Li, Guoyin and Tam, Matthew K (2015) Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity. (Submitted)

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    Abstract

    In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H ̈older regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii– Mann iterations, the cyclic projection algorithm, and the Douglas–Rachford feasibility algorithm along with some variants. In the important case in which the underlying sets are convex sets described by convex polynomials in a finite dimensional space, we show that the H ̈older regularity properties are automatically satisfied, from which sublinear convergence follows.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 28 Mar 2016 12:13
    Last Modified: 28 Mar 2016 12:13
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1690

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