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arXiv · 1609.02928

Algorithmic construction of the subdifferential from directional derivatives

Charles Audet·Warren Hare
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Abstract

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 $\R^1$ and $\R^2$, as well as in $\R^n$ where subdifferential is known to possess at most three vertices.

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Charles Audet, Warren Hare. 2016-09-09. Algorithmic construction of the subdifferential from directional derivatives. https://arxiv.org/abs/1609.02928

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