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Partially smooth variational principles and applications. (English) Zbl 0927.49010
Consider an extended-real-valued lower-semicontinuous proper function \(f\) defined on a Banach space \(X\). Let \(Y\subset X\) be a subspace equipped with a bornology \(\beta\). The authors introduce the concept of \(\beta\)-viscosity subdifferential of \(f\) relative to \(Y\). They show how this concept allows us to establish a great variety of theorems pertaining to the realm of nonsmooth analysis (Borwein-Preiss variational principle, fuzzy sum rule, Zagrodny’s mean value theorem, Clarke-Ledyaev mean value inequality, Kruger-Mordukhovich extremal principle,…).
Reviewer: A.Seeger (Avignon)

MSC:
49J52 Nonsmooth analysis
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