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G-2016-12

Algorithmic construction of the subdifferential from directional derivatives

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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

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Publication

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Set-Valued and Variational Analysis, 26(3), 431–447, 2018 référence BibTeX