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About stationarity and regularity in variational analysis. (English) Zbl 1223.90075

Summary: Stationarity and regularity concepts are investigated for the three classes of objects which are typical for variational analysis – real-valued functions, collections of sets, and multifunctions. 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 equivalent in a sense. 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.

MSC:

90C46 Optimality conditions and duality in mathematical programming
90C48 Programming in abstract spaces
49K27 Optimality conditions for problems in abstract spaces
58E30 Variational principles in infinite-dimensional spaces
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