Algorithmic construction of the subdifferential from directional derivatives

The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes algorithms to reconstruct a polyhedral subdifferential of a function from the computation of finitely many directional derivatives. We provide upper bounds on the required number of directional derivatives when the space is ${\mathbb{R}}^1$ and ${\mathbb{R}}^2$, as well as in ${\mathbb{R}}^n$ where subdifferential is known to possess at most three vertices.