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Zbl 0866.49024
Mordukhovich, Boris S.; Shao, Yongheng
Nonconvex differential calculus for infinite-dimensional multifunctions.
(English)
[J] Set-Valued Anal. 4, No.3, 205-236 (1996). ISSN 0927-6947; ISSN 1572-932X/e

The authors start from a notion of normal cone built by means of Fréchet $\varepsilon$-normals and a procedure of sequential upper limit. Then they build a related notion of coderivative for a multifunction $F$ from a Banach space $X$ to another Banach space $Y$. When $X$ and $Y$ are both Asplund spaces, such a notion turns out to have a rich calculus. Their approach should be compared with that of {\it A. D. Ioffe} [Mathematika 36, No. 1, 1-38 (1989; Zbl 0713.49022)], which is otherwise based on topological upper limits. In the particular case of an extended real-valued function $\varphi:X\to \overline{\bbfR}$, corresponding notions have been introduced by the same authors in J. Convex Anal. 2, No. 1-2, 211-227 (1995; Zbl 0838.49013).
[M.Degiovanni (Brescia)]
MSC 2000:
*49J52 Nonsmooth analysis (other weak concepts of optimality)
58C06 Set-valued mappings etc. on manifolds
58C20 Generalized differentiation theory on manifolds

Keywords: nonconvex subdifferentials; Banach spaces; Asplund spaces

Citations: Zbl 0713.49022; Zbl 0838.49013

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