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Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure.
In: Journal of Optimization Theory and Applications.
Bd. 160
(2014)
Heft 2
.
- S. 391-414.
ISSN 0022-3239
DOI: https://doi.org/10.1007/s10957-013-0401-x
| Rez.: |
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| Projektfinanzierung: |
The Hermann Minkowski Center for Geometry at Tel Aviv University, Tel Aviv, Israel
and University of Ballarat ‘Self-sustaining Regions Research and Innovation Initiative’, an Australian Government Collaborative Research Network (CRN) |
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Abstract
We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the delta-convex structure of the function. The new definition extends to a more general class of functions, which includes Lipschitz functions definable on $o$-minimal structure and quasidifferentiable functions.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Zusätzliche Informationen: | Contents:
1. Introduction 2. Directed Sets – a Brief Overview 3. The Directed Subdifferential with Known Delta-Convex Structure 4. The Directed Subdifferential Without a Delta-Convex Structure 4.1 Convex Functions 4.2 Delta-Convex and Quasidifferentiable Functions 5. Extension of the Directed Subdifferential 5.1 Directed Subdifferentiable Functions 5.2 Extension to Directed Subdifferentiable Functions 5.3 The Class of Directed Subdifferentiable Functions 6. Conclusions published in arXiv at December 2012 and in JOTA Online First at September 2013; |
| Keywords: | nonconvex subdifferentials; directional derivatives; difference of convex (delta-convex, DC) functions; differences of sets |
| Fachklassifikationen: | Mathematics Subject Classification Code: 49J52 (90C26 26B25 58C20) |
| Institutionen der Universität: | Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder Profilfelder > Advanced Fields Profilfelder > Advanced Fields > Nichtlineare Dynamik |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 29 Jan 2015 07:11 |
| Letzte Änderung: | 01 Sep 2015 10:03 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/6117 |