Geodesic
Stability of Closedness of Convex Cones under Linear Mappings
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 699-705
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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.
Classification : 47N10, 90C25, 90C22
Mots-clés : Closed convex cone, linear mapping, stability, linear programming 
@article{JCA_2009_16_3_JCA_2009_16_3_a6,
     author = {J. M. Borwein and W. B. Moors},
     title = {Stability of {Closedness} of {Convex} {Cones} under {Linear} {Mappings}},
     journal = {Journal of convex analysis},
     pages = {699--705},
     year = {2009},
     volume = {16},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a6/}
}
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J. M. Borwein; W. B. Moors. Stability of Closedness of Convex Cones under Linear Mappings. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 699-705. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a6/