Lets

f : S⊂Rn → R

It is said that X is subgradient of f at y if for all x point of S it is holds

f(x) ≥ f(y) + X(x-y)

Ie function graph That is, the graph of the function lies above the space generated by the gradient

Note 1: In the case of a concave function subgradient is defined equaly, only the changing ≥ by ≤.

Note 2: Note that definition does not required to be differentiability.

Note 3: The subgradient need not be unique.