Geodesic
Stability of Closedness of Closed Convex Sets under Linear Mappings
Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1281-1291
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We study the problem of when the linear image of a fixed closed convex subset X of Rn is closed. Specifically, we improve results of J. M. Borwein and W. B. Moors [Stability of closedness of convex cones under linear mappings I, J. Convex Analysis 16 (2009) 699--705; Stability of closedness of convex cones under linear mappings II, J. Nonlinear Analysis Optim. 1 (2010) 1--7] by showing that for almost all linear mappings T from Rn into Rm, not only T(X) is closed, but there is also an open neighborhood of T whose members also preserve the closedness of X.
Classification : 47N10, 90C25, 90C22
Mots-clés : Asymptotic cone, closedness, convex cone, convex set, linear mapping, stability, sigma-porosity 
@article{JCA_2021_28_4_JCA_2021_28_4_a16,
     author = {S. T. Dinh and T.-S. Pham},
     title = {Stability of {Closedness} of {Closed} {Convex} {Sets} under {Linear} {Mappings}},
     journal = {Journal of convex analysis},
     pages = {1281--1291},
     year = {2021},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a16/}
}
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S. T. Dinh; T.-S. Pham. Stability of Closedness of Closed Convex Sets under Linear Mappings. Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1281-1291. http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a16/