Journal of Convex Analysis 34 (2027), No. 1, 129--141
Copyright Heldermann Verlag 2027
New Characterizations of Strong Convexity
Chadi Nour
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
cnour@lau.edu.lb
Jean Takche
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
jtakchi@lau.edu.lb
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.
Keywords: Strong convexity, prox-regularity, exterior sphere condition, S-convexity, epi-Lipschitz property, convex analysis, nonsmooth analysis, proximal analysis.
MSC: 52A20, 49J52, 49J53.
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