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Stability of closedness of convex cones under linear mappings II

Borwein, Jonathan M. and Moors, Warren B. (2010) Stability of closedness of convex cones under linear mappings II. Journal of Nonlinear Analysis and Optimization: Theory and Applications, 1 (1). pp. 1-7.

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    Abstract

    In this paper we revisit the question of when the continuous linear image of a fixed closed convex cone K is closed. Specifically, we improve the main result of 3 by showing that for all, except for at most a $\sigma-$porous set, of the linear mappings T from $\mathbb{R}^n$ into $\mathbb{R}^m$, not only is T(K) closed, but there is also a neighbourhood around T whose members also preserve the closedness of K.

    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 15:28
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1226

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