Abstract

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.

Author information

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Keywords

  • Variational analysis
  • strong convexity
  • prox-regularity
  • farthest distance function
  • semiconvexity

Mathematics Subject Classification

49J52, 49J53

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Suggested citation

F. Nacry, V. A. T. Nguyen, L. Thibault. “Farthest Distance Function to Strongly Convex Sets.” Journal of Convex Analysis 30 (2023), No. 4, 1217–1240. https://doi.org/10.68381/jca30055

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