Questions tagged [non-smooth-analysis]

The theory that develops differential calculus for functions that are not differentiable in the usual sense.

91 questions
3
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Relationship between Clarke-subdifferential $\partial_{C}f(\, \cdot \,)$ and Bouligand-subdifferential $\partial_{B}f(\, \cdot \,)$

Let $f: \mathbb{R}^{n} \rightarrow \mathbb{R}$ be locally Lipschitz sontinuous. (1) The Clarke-subdifferential $\partial_{C} f(x) \subset \mathbb{R}^{n}$ of $f$ in $x \in \mathbb{R}^{n}$ is defined by \begin{equation*}…
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How to find the subdifferential of $|x|$?

I want to compute the subdifferential of $ f $ on $ \mathbb{R} \setminus \{ 0 \} $ when $ f(x) = |x| $. How do I do this?