Title :
Generalized derivatives of generalized distance functions and the existence of generalized nearest points
Author :
Luo, Xian-fa ; He, Jin-su
Author_Institution :
Dept. of Math., China Jiliang Univ., Hangzhou, China
Abstract :
This note investigates the relationships between the generalized directional derivatives of the generalized distance function and the existence of the generalized nearest points in Banach spaces. It is proved that the generalized distance function associated with a closed bounded convex set having the Clark, Michel-Penot, Dini, or modified Dini derivative equals to 1 or -1 implies the existence of generalized nearest points. Also, new characterization theorems of (compact) locally uniformly sets are obtained.
Keywords :
Banach spaces; set theory; Banach spaces; Clark derivative; Michel-Penot derivative; closed bounded convex set; generalized directional derivatives; generalized distance function; generalized nearest points; modified Dini derivative; Generalized derivatives; compactly locally uniform convexity; generalized distance function; generalized nearest point;
Conference_Titel :
Machine Learning and Cybernetics (ICMLC), 2011 International Conference on
Conference_Location :
Guilin
Print_ISBN :
978-1-4577-0305-8
DOI :
10.1109/ICMLC.2011.6016815