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A Cyclic Douglas-Rachford Iteration Scheme

Tam, Matthew K and Borwein, Jonathan M. (2013) A Cyclic Douglas-Rachford Iteration Scheme. Journal of Optimization Theory and Applications .

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    Abstract

    In this paper we present two Douglas--Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas--Rachford scheme, are promising.

    Item Type: Article
    Additional Information: For interactive Cinderella applets visit http://carma.newcastle.edu.au/tam/cycdr/
    Subjects: 46-xx Functional analysis > 46Txx Nonlinear functional analysis
    49-xx Calculus of variations and optimal control; optimization
    90-xx Economics, operations research, programming, games
    Faculty: UNSPECIFIED
    Depositing User: Mr Matthew K Tam
    Date Deposited: 26 Apr 2013 11:47
    Last Modified: 28 Nov 2014 15:09
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1469

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