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Stability of closedness of convex cones under linear mappings

Borwein, Jonathan M. and Moors, Warren B. (2009) Stability of closedness of convex cones under linear mappings. Journal of Convex Analysis, 16 (3-4). pp. 707-713.

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    Abstract

    In this paper we reconsider the question of when the continuous linear image of a closed convex cone is closed in Euclidean space. In particular, we show that although it is not true that the closedness of the image is preserved under small perturbations of the linear mappings it is “almost” true that the closedness of the image is preserved under small perturbations, in the sense that, for “almost all” linear mappings from $R^n$ into $R^m$ if the image of the cone is closed then there is a small neighbourhood around it whose members also preserve the closedness of the cone.

    Item Type: Article
    Uncontrolled Keywords: closed convex cone, linear mapping, stability, linear programming
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 05 Jan 2015 16:05
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1229

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