
Journal of Convex Analysis 16 (2009), No. 3, 699705 Copyright Heldermann Verlag 2009 Stability of Closedness of Convex Cones under Linear Mappings Jonathan M. Borwein Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia B3H 1W5, Canada jborwein@cs.dal.ca Warren B. Moors Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand moors@math.auckland.ac.nz 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. Keywords: Closed convex cone, linear mapping, stability, linear programming. MSC: 47N10; 90C25, 90C22 [ Fulltextpdf (108 KB)] for subscribers only. 