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Subdifferential Regularity of Directionally Lipschitzian Functions

Published online by Cambridge University Press:  20 November 2018

M. Bounkhel  and
L. Thibault
M. Bounkhel
Affiliation:
Laboratoire d’Analyse Convexe Case Courier 051 Université Montpellier II 34095 Montpellier France
L. Thibault
Affiliation:
Laboratoire d’Analyse Convexe Case Courier 051 Université Montpellier II 34095 Montpellier France
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Abstract

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Formulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established.

Keywords

49J5258C2049J5090C26subdifferential regularitydirectional regularitydirectionally Lipschitzian functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 25 - 36
Copyright
Copyright © Canadian Mathematical Society 2000

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