Infinite dimensional clarke generalized Jacobian

Z. Páles, Vera Zeidan

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper we extend for a locally Lipschitz function the notion of Clarke's generalized Jacobian to the setting where the domain lies in an infinite dimensional normed space. When the function is real-valued this notion reduces to the Clarke's generalized gradient. Using this extension, we obtain an exact smooth-nonsmooth chain rule from which the sum rule and the product rule follow. Also an exact formula for the generalized Jacobian of piecewise differentiable functions will be provided.

Original languageEnglish
Pages (from-to)433-454
Number of pages22
JournalJournal of Convex Analysis
Volume14
Issue number2
Publication statusPublished - 2007

Fingerprint

Generalized Jacobian
Clarke's Generalized Gradient
Product rule
Locally Lipschitz Function
Chain rule
Infinite-dimensional Spaces
Sum Rules
Normed Space
Differentiable

Keywords

  • Chain rule
  • Generalized jacobian
  • Piecewise smooth functions
  • Sum rule

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Infinite dimensional clarke generalized Jacobian. / Páles, Z.; Zeidan, Vera.

In: Journal of Convex Analysis, Vol. 14, No. 2, 2007, p. 433-454.

Research output: Contribution to journalArticle

Páles, Z. ; Zeidan, Vera. / Infinite dimensional clarke generalized Jacobian. In: Journal of Convex Analysis. 2007 ; Vol. 14, No. 2. pp. 433-454.
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