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On concepts of directional differentiability. (English) Zbl 0682.49015
Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of \(\sigma\)-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.
Reviewer: A.Shapiro

MSC:
49J52 Nonsmooth analysis
26B05 Continuity and differentiation questions
46G05 Derivatives of functions in infinite-dimensional spaces
49J50 Fréchet and Gateaux differentiability in optimization
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