- Title
- Convergence rate analysis for averaged fixed point iterations in common fixed point problems
- Creator
- Borwein, Jonathan M.; Li, Guoyin; Tam, Matthew K.
- Relation
- Funding BodyARCGrant NumberDP160101537 http://purl.org/au-research/grants/arc/DP160101537
- Relation
- SIAM Journal on Optimization Vol. 27, Issue 1, p. 1-33
- Publisher Link
- http://dx.doi.org/10.1137/15M1045223
- Publisher
- Society for Industrial and Applied Mathematics
- Resource Type
- journal article
- Date
- 2017
- Description
- 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 Hölder 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 many important iterative methods in solving broad mathematical problems such as convex feasibility problems and variational inequality problems. These include Krasnoselskii-Mann iterations, the cyclic projection algorithm, forward-backward splitting 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 Hölder regularity properties are automatically satisfied, from which sublinear convergence follows.
- Subject
- averaged operator; fixed point iteration; convergence rate; Hölder regularity; semi-algebraic; Douglas-Rachford algorithm
- Identifier
- http://hdl.handle.net/1959.13/1387455
- Identifier
- uon:32608
- Identifier
- ISSN:1052-6234
- Language
- eng
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