Links between directional derivatives through multidirectional mean value inequalities

Rafael Correa, Pedro Gajardo, Lionel Thibault

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel et al., SIAM J Optim 9(3), 690-706 (1999)]. © 2007 Springer-Verlag.
Original languageEnglish
Pages (from-to)57-77
Number of pages21
JournalMathematical Programming
DOIs
Publication statusPublished - 1 Jan 2009

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