The quasidifferential calculus, separation of convex sets and the Demyanov difference

Abstract

In this paper we give a survey of the influence of the quasidifferential calculus of V. F. Demyanov and A. M. Rubinov to the field of generalized convexity. In particular, we will show the strong relations between the order cancellation property of bounded closed convex set and the separation property of bounded closed convex sets by sets. Moreover, a generalization of the Demyanov difference of compact convex sets infinite dimension and its role in the context of convex sets by sets is discussed. Refs 15. Figs 2.