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Subdifferential representation formula and subdifferential criteria for the behavior of nonsmooth functions

✍ Scribed by Rafael Correa; Pedro Gajardo; Lionel Thibault

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 424 KB
Volume: 65
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2005.10.003

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✦ Synopsis

Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be equivalent to certain appropriate conditions in terms of the Clarke subdifferential. The paper provides a systematic study showing that any such condition with the Clarke subdifferential is valid if and only if it holds with any operator representing the Clarke subdifferential like in the subdifferential proximal formula.

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✍ Radu Ioan Boţ; Sorin-Mihai Grad; Gert Wanka 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 248 KB 👁 1 views

## Abstract In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also __K__ ‐increa