Journal of Convex Analysis 16 (2009), No. 2, 501--514
Copyright Heldermann Verlag 2009
Proximal Smoothness and the Exterior Sphere Condition
Chadi Nour
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus, Lebanon
cnour@lau.edu.lb
Ron J. Stern
Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada
stern@mathstat.concordia.ca
Jean Takche
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus, Lebanon
jtakchi@lau.edu.lb
Proximal smoothness and the exterior sphere condition are compared. It is shown via examples that these two properties are not necessarily equivalent, and geometric conditions are provided under which the equivalence holds.
Keywords: Proximal smoothness, interior and exterior sphere conditions, wedged sets, proximal analysis, nonsmooth analysis.
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