I was interested in learning and understanding sub gradients as much as I could from some good resource.
I know what the definition is, but I seem unable to apply the definition to prove basic facts about it.
For example, some properties I would be interested in proving is that the sub-gradient is additive and that it satisfies the chain rule and any other property that it satisfies.
I would be also interested to see the sub gradient used to solve problems, maybe in the context of convex optimization, like finding the global minimizer etc.
For example, I was trying to find the sub gradient of:
$$R(w) = \sum^{d}_{j=1} |w_j|$$
I was told that the answer is:
$$\partial R(w) = (\partial R(w_1), ..., \partial R(w_d) )$$
However, I think I lack the basic understanding of these techniques to do it myself, and would like to make myself self sufficient so that I don't have to resort to math.stackexchange every time I have a basic question about sub gradient. I feel these are questions I should be able to answer on my own if I understood it properly and so I was looking for a good book to learn sub gradients from (preferably with an emphasis to convex optimization, but thats just a plus if its possible).
The resources so far that I have been able to find are slides from university classes (which are no really the type of thing that I was looking for). The best thing I found was the following paper:
https://web.stanford.edu/class/ee392o/subgrad_method.pdf
it seems to be focused more on its application to solve convex optimization problem, which is great! But, I still don't feel self sufficient enough with respect to the sub gradient, so its not trivial for me follow it fully.