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Nonconvex differential calculus for infinite-dimensional multifunctions. (English) Zbl 0866.49024
The authors start from a notion of normal cone built by means of Fréchet ε-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 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 φ:X ¯, corresponding notions have been introduced by the same authors in J. Convex Anal. 2, No. 1-2, 211-227 (1995; Zbl 0838.49013).
49J52Nonsmooth analysis (other weak concepts of optimality)
58C06Set-valued and function-space valued mappings on manifolds
58C20Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
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