About Stationarity and Regularity in Variational Analysis

Stationarity and regularity concepts for the three typical for variational analysis classes of objects – real-valued functions, collections of sets, and multifunctions – are investigated. An attempt is maid to present a classification scheme for such concepts and to show that properties introduced for objects from different classes can be treated in a similar way. Furthermore, in many cases the corresponding properties appear to be in a sense equivalent. The properties are defined in terms of certain constants which in the case of regularity properties provide also some quantitative characterizations of these properties. The relations between different constants and properties are discussed. An important feature of the new variational techniques is that they can handle nonsmooth functions, sets and multifunctions equally well Borwein and Zhu [8] 3