Infinite dimensional generalized Jacobian: Properties and calculus rules

The extension to infinite dimensional domains of Clarke's generalized Jacobian is the focus of this paper. First, a generalization of a Fabian–Preiss theorem to the infinite dimensional setting is obtained. As a consequence, a new formula relating the Clarke's generalized Jacobians corresp...

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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 344; H. 1; S. 55 - 75
Hauptverfasser: Páles, Zsolt, Zeidan, Vera
Format: Journal Article
Sprache:Englisch
Veröffentlicht: San Diego, CA Elsevier Inc 01.08.2008
Elsevier
Schlagworte:
Chain rule
Characterization of the generalized Jacobian
Exact sciences and technology
Formula for a continuous selection
Generalized Jacobian
Mathematical analysis
Mathematics
Sciences and techniques of general use
Sum rule
Characterization of the generalized Jacobian
Chain rule
Formula for a continuous selection
Sum rule
Generalized Jacobian
Mathematical analysis
Application
ISSN:0022-247X, 1096-0813
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Zusammenfassung:The extension to infinite dimensional domains of Clarke's generalized Jacobian is the focus of this paper. First, a generalization of a Fabian–Preiss theorem to the infinite dimensional setting is obtained. As a consequence, a new formula relating the Clarke's generalized Jacobians corresponding to finite dimensional spaces K, L with K ⊆ L is established. Furthermore, in the infinite dimensional case, basic properties pertaining the generalized Jacobian are developed and then an identification of this set-valued map is produced. Applications of these results in the form of chain rules including sum and product rules, and a computational formula for continuous selections are derived.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.02.044