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Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 431–447 | Cite as

Algorithmic Construction of the Subdifferential from Directional Derivatives

  • Charles Audet
  • Warren Hare
Article

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 ℝ1 and ℝ2, as well as in ℝ n where subdifferential is known to possess at most three vertices.

Keywords

Subdifferential Directional derivative Polyhedral construction Geometric probing 

Mathematics Subject Classification (2010)

Primary; 52B12 65K15 Secondary; 49M37 90C30 90C56 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Département de mathématiques et génie industrielÉcole Polytechnique de MontréalMontréalCanada
  2. 2.Mathematics, Irving K. Barber SchoolUniversity of British ColumbiaKelownaCanada

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