Borwein, Jonathan M.; Treiman, Jay S.; Zhu, Qiji J. Partially smooth variational principles and applications. (English) Zbl 0927.49010 Nonlinear Anal., Theory Methods Appl. 35, No. 8, B, 1031-1059 (1999). 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) Cited in 5 Documents MSC: 49J52 Nonsmooth analysis Keywords:generalized subdifferential; \(\beta\)-viscosity subdifferential; nonsmooth analysis PDFBibTeX XMLCite \textit{J. M. Borwein} et al., Nonlinear Anal., Theory Methods Appl. 35, No. 8, 1031--1059 (1999; Zbl 0927.49010) Full Text: DOI