Groupe d’études et de recherche en analyse des décisions

# Algorithmic construction of the subdifferential from directional derivatives

## Charles Audet et Warren Hare

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.

, 20 pages