Choquet theorem and nonsmooth analysis
type: Item
instance of: scholarly article
title: Choquet theorem and nonsmooth analysis
zbMATH Open document ID: 0679.49015
author: Shuzhong Shi
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1988-01-01T00:00:00Z
review text: It is shown that a classical theorem of \textit{G. Choquet} [Ann. Univ. Grenoble, Sect. Sci. Math. Phys. II. Sér. 23, 57-112 (1948; Zbl 0031.28101)] (stating the generic equality between the contingent and the paratingent cones to a subset of a separable Banach space) has several applications to nonsmooth analysis. In particular, it is proved that if an open subset of a separable Banach space is generically tangentially regular (i.e. regular in the sense of \textit{F. H. Clarke} [Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]) on its boundary, then its contingent cone is generically equal to a closed halfspace. Next, it is shown that for a continuous function on an open subset of a separable Banach space, the subdifferential regularity, the regular Gâteaux differentiability and the strict differentiability in the full limit sense are generically equivalent.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 4113374
zbMATH Keywords: contingent and the paratingent cones
zbMATH Keywords: generically tangentially regular
zbMATH Keywords: subdifferential regularity
zbMATH Keywords: regular Gâteaux differentiability
zbMATH Keywords: strict differentiability
reviewed by: Marcin Studniarski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4113374