# Questions tagged [non-smooth-analysis]

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

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### When is upper/lower Dini derivative finite?

Consider a function $f:\mathbb{R}\rightarrow \mathbb{R}$. Lower right Dini derivative is defined as $D_+f(x)=\liminf_{t\rightarrow 0+}\cfrac{f(x+th)-f(x)}{h}$ (Also, the Wiki link for the definition ...
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### For a Lipschitz function, is the gradient (when defined) orthogonal to level set?

For a differentiable function f, we know that the gradient is orthogonal to the level sets of f. What if f is Lipschitz continuous? we know that its gradient exists almost everywhere. Is the gradient (...
• 450
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### Fundamental Theorem of Calculus for non-differentiable convex functions

Suppose $C\subset\mathbb{R}^n$ is a convex set and $f:C\to\mathbb{R}$ is a convex function. I wonder if the following statement is true. Suppose $g:C\to\mathbb{R}^n$ satisfies $g(x)\in\partial f(x)$ ...
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### Proof of Theorem 6.14 in "Variational analysis (Rockafellar, Wets)"

I am currently reading "Variational analysis" by Rockafellar and Wets, and I am trying to understand the proof of Theorem 6.14 about normal cones to sets with constraint structure. But, I ...
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### Subgradient of the spectral norm

I am working on developing a numerical algorithm that needs to use a subgradient of $\|\cdot\|_2$ (matrix norm) at each iteration. According to Characterization of the Subdifferential of Some Matrix ...
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### Some basic subdifferential computations

I'm trying to understand a bit of nonsmooth analysis, but I'm struggling even to compute a simple example. Any help would be awesome! Could you please confirm how do the subdifferentials of these ...
• 432
1 vote