On concepts of directional differentiability |
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Authors: | A. Shapiro |
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Affiliation: | (1) Department of Mathematics and Applied Mathematics, University of South Africa, Pretoria, Republic of South Africa |
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Abstract: | 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 -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. |
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Keywords: | Directional derivatives positively homogeneous mapping locally Lipschitz mapping chain rule |
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