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Linear regularity for an infinite system formed by \(p\)-uniformly subsmooth sets in Banach spaces. (English) Zbl 1235.90155

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.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C25 Convex programming
49J52 Nonsmooth analysis
46B20 Geometry and structure of normed linear spaces
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