Title

On a nonconvex separation theorem and the approximate extremal principle in Asplund spaces.

Document Type

Conference Paper in Published Proceedings

Department

Mathematics and Computer Science

Publication Date

2013

Abstract

In this paper we establish a revised version of the {\em nonconvex separation theorem} established in [J.M. Borwein and A. Jofr\'{e}, A nonconvex separation property in Banach spaces, Math. Meth. Oper. Res. {\bf 48} 169--179 (1996)]. Our new separation theorem is formulated in terms of Fr\'echet normal cones in Asplund spaces while theirs was formed with an abstract kind of generalized differentiation enjoying a good calculus. It is, indeed, shown to be equivalent to the known {\em approximate extremal principle} in [B. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series (Fundamental Principles of Mathematical Sciences) {\bf 330}, Springer, Berlin (2006)]. In addition, we discuss several efficient conditions ensuring the extremality property of a system of nonconvex sets.

http://link.springer.com/article/10.1007%2Fs40306-013-0018-z

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