Wei, Zhou Linear regularity for an infinite system formed by \(p\)-uniformly subsmooth sets in Banach spaces. (English) Zbl 1235.90155 Taiwanese J. Math. 16, No. 1, 335-352 (2012). Summary: We introduce and study \(p\)-uniform subsmoothness of a collection of infinitely many closed sets in a Banach space. Using variational analysis and techniques, we mainly study linear regularity for a collection of infinitely many closed sets satisfying \(p\)-uniform subsmoothness. The necessary or/and sufficient conditions on the linear regularity are obtained in this case. In particular, we extend the characterizations of linear regularity for a collection of infinitely many closed convex sets to the nonconvex setting. Cited in 3 Documents MSC: 90C31 Sensitivity, stability, parametric optimization 90C25 Convex programming 49J52 Nonsmooth analysis 46B20 Geometry and structure of normed linear spaces Keywords:linear regularity; subsmoothness; Clarke subdifferential; normal cone; Asplund space PDFBibTeX XMLCite \textit{Z. Wei}, Taiwanese J. Math. 16, No. 1, 335--352 (2012; Zbl 1235.90155) Full Text: DOI Link