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Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure

Title data

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure.
In: Journal of Optimization Theory and Applications. Vol. 160 (2014) Issue 2 . - pp. 391-414.
ISSN 0022-3239
DOI: https://doi.org/10.1007/s10957-013-0401-x

Review:

Official URL: Volltext

Project information

Project financing: 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)

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: 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
Subject classification: Mathematics Subject Classification Code: 49J52 (90C26 26B25 58C20)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 29 Jan 2015 07:11
Last Modified: 01 Sep 2015 10:03
URI: https://eref.uni-bayreuth.de/id/eprint/6117