Choquet theorem and nonsmooth analysis
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.
scientific article; zbMATH DE number 4113374