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The Douglas-Rachford algorithm in the absence of convexity

Borwein, Jonathan M. and Sims, Brailey (2011) The Douglas-Rachford algorithm in the absence of convexity. In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer Optimization and Its Applications (49). Springer. ISBN 978-1-4419-9568-1 (In Press)

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    Abstract

    The Douglas-Rachford iteration scheme, introduced half a century ago in connection with nonlinear heat ow problems, aims to find a point common to two or more closed constraint sets. Convergence of the scheme is ensured when the sets are convex subsets of a Hilbert space, however, despite the absence of satisfactory theoretical justification, the scheme has been routinely used to successfully solve a diversity of practical problems in which one or more of the constraints involved is non-convex. As a first step toward addressing this deficiency, we provide convergence results for a prototypical non-convex two-set scenario in which one of the sets is the Euclidean sphere.

    Item Type: Book Section
    Subjects: 40-xx Sequences, series, summability > 40Axx Convergence and divergence of infinite limiting processes
    46-xx Functional analysis > 46Txx Nonlinear functional analysis
    49-xx Calculus of variations and optimal control; optimization > 49Mxx Methods of successive approximations
    Faculty: UNSPECIFIED
    Depositing User: eduardo castillo
    Date Deposited: 13 Dec 2010 11:51
    Last Modified: 06 Apr 2011 16:28
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/770

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