Abstract

Parallel to the main results of C. Nour, R. J. Stern and J. Takche in " Proximal smoothness and the exterior sphere condition" [J. Convex Analysis 16/2 (2009) 501–514] and of C. Nour and J. Takche in "A new class of sets regularity" [J. Convex Analysis 25/4 (2018) 1059–1074], which explore the equivalence between prox-regularity, the exterior sphere condition, and S-convexity, we present novel characterizations of the r-strong convexity property, namely, of the sets that can be expressed as the intersection of closed balls with the same radius r > 0

Author information

Contact details are reproduced from the original publication and may be historical.

Chadi Nour

Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon

cnour@lau.edu.lb

Jean Takche

Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon

jtakchi@lau.edu.lb

Keywords

  • Strong convexity
  • prox-regularity
  • exterior sphere condition
  • S-convexity
  • epi-Lipschitz property
  • convex analysis
  • nonsmooth analysis
  • proximal analysis

Mathematics Subject Classification

52A20, 49J52, 49J53

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Suggested citation

C. Nour, J. Takche. “New Characterizations of Strong Convexity.” Journal of Convex Analysis 34 (2027), No. 1, 96–105. https://doi.org/10.68381/jca34007

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