Higher order directional derivatives for nonsmooth functions (Q2762969)
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scientific article; zbMATH DE number 1689818
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Higher order directional derivatives for nonsmooth functions |
scientific article; zbMATH DE number 1689818 |
Statements
16 January 2002
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Fréchet derivative
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nonsmooth function
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convex function
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0.93919635
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0.9261406
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0.9072322
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0.9068959
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0.90442145
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0.8995296
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Higher order directional derivatives for nonsmooth functions (English)
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The authors of the paper under consideration propose a definition of higher order lower and upper directional derivatives of a real valued function \(f\) defined on a real normed space. It is proved that if \(f\) is respectable times Fréchet differentiable then these derivatives coincide with the corresponding higher order lower derivatives. A class of convex functions is characterized in Theorem 3. Theorem 4 deals with second order Taylor expansion for Fréchet differentiable functions.
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