Geodesic
Farthest Distance Function to Strongly Convex Sets
Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1217-124
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The aim of the present paper is twofold. On one hand, we show that the strong convexity of a set is equivalent to the semiconcavity of its associated farthest distance function. On the other hand, we establish that the farthest distance of a point from a strongly convex set is the minimum of farthest distances of the given point from suitable closed balls separating the set and the point. Various other results on strongly convex sets are also provided.
Classification : 49J52, 49J53
Mots-clés : Variational analysis, strong convexity, prox-regularity, farthest distance function, semiconvexity 
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     author = {F. Nacry and V. A. T. Nguyen and L. Thibault},
     title = {Farthest {Distance} {Function} to {Strongly} {Convex} {Sets}},
     journal = {Journal of convex analysis},
     pages = {1217--124},
     year = {2023},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a6/}
}
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F. Nacry; V. A. T. Nguyen; L. Thibault. Farthest Distance Function to Strongly Convex Sets. Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1217-124. http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a6/