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Uniformity and inexact version of a proximal method for metrically regular mappings

Aragón Artacho, Francisco J. and Geoffroy, Michel H. (2007) Uniformity and inexact version of a proximal method for metrically regular mappings. Journal of Mathematical Analysis and Applications., 335 (1). pp. 168-183. ISSN 0022-247X

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    Abstract

    We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact proximal point method for strongly metrically subregular mappings and show that it is super-linearly convergent to a solution to the inclusion 0 ∈ T (x).

    Item Type: Article
    Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
    90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
    Faculty: UNSPECIFIED
    Depositing User: Dr. Francisco Javier Aragón Artacho
    Date Deposited: 06 Sep 2011 15:45
    Last Modified: 06 Sep 2011 15:45
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/916

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