Deakin University
Browse

File(s) under permanent embargo

Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples

Version 2 2024-06-05, 06:39
Version 1 2021-07-06, 08:13
conference contribution
posted on 2024-06-05, 06:39 authored by Reinier Diaz MillanReinier Diaz Millan, SB Lindstrom, V Roshchina
We focus on the convergence analysis of averaged relaxations of cutters, specifically for variants that—depending upon how parameters are chosen—resemble alternating projections, the Douglas–Rachford method, relaxed reflect-reflect, or the Peaceman–Rachford method. Such methods are frequently used to solve convex feasibility problems. The standard convergence analysis of projection algorithms is based on the firm nonexpansivity property of the relevant operators. However, if the projections onto the constraint sets are replaced by cutters (which may be thought of as maps that project onto separating hyperplanes), the firm nonexpansivity is lost. We provide a proof of convergence for a family of related averaged relaxed cutter methods under reasonable assumptions, relying on a simple geometric argument. This allows us to clarify fine details related to the allowable choice of the relaxation parameters, highlighting the distinction between the exact (firmly nonexpansive) and approximate (strongly quasinonexpansive) settings. We provide illustrative examples and discuss practical implementations of the method.

History

Volume

313

Pagination

75-98

Location

Newcastle, N.S.W.

Start date

2017-09-25

End date

2017-09-29

ISBN-13

9783030365684

ISBN-10

3030365689

Language

eng

Publication classification

E1.1 Full written paper - refereed

Title of proceedings

JBCC 2017 : From Analysis to Visualization A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017

Event

From Analysis to Visualization. Conference (2017 : Newcastle, New South Wales)

Publisher

Springer

Place of publication

Cham, Switzerland

Series

Springer Proceedings in Mathematics & Statistics

Usage metrics

    Research Publications

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC