Acta Mathematica Vietnamica


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


In this paper we establish a revised version of the nonconvex separation theorem established in J.M. Borwein and A. Jofré (Math. Meth. Oper. Res. 48:169–179, 1996). Our new separation theorem is formulated in terms of Fréchet normal cones in Asplund spaces while their result was formed with an abstract kind of generalized differentiation enjoying a good calculus. It is, indeed, shown to be equivalent to the known approximate extremal principle in B. Mordukhovich (Variational analysis and generalized differentiation, I: Basic theory, Grundlehren series 330, Springer, Berlin, 2006). In addition, we discuss several efficient conditions ensuring the extremality property of a system of nonconvex sets.

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