Stability of closedness of convex cones under linear mappings

Title: Stability of closedness of convex cones under linear mappings
Creator: Borwein, Jonathan M.; Moors, Warren B.
Relation: Journal of Convex Analysis Vol. 16, Issue 3-4, p. 699-705
Relation: http://www.heldermann.de/JCA/JCA16/JCA163/jca16041.htm
Publisher: Heldermann Verlag
Resource Type: journal article
Date: 2009
Description: 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 ℝn into ℝm 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.
Subject: closed convex cone; linear mapping; stability; linear programming
Identifier: uon:7182
Identifier: http://hdl.handle.net/1959.13/806655
Identifier: ISSN:0944-6532
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