It is obvious that there is similarity between subgradient and gradient. The subgradient of smooth functions is reduced to gradient. I have two questions.
The first is does there exist subgradient decent method (analogous to the well known gradient decent mothod) in nonsmooth problems.
The second is, given a nonsmooth function, how to determine the subgradient? (by computer)
Summarily, I have no idea of the role of subgradient in programming of nonsmooth functions. Is it just a concept or a very useful tool (like gradient)?