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The Directed Subdifferential of DC functions

Titelangaben

Baier, Robert ; Farkhi, Elza:
The Directed Subdifferential of DC functions.
Hausdorff-Research-Institute
Bonn , 2008 . - 19 S.

Volltext

Link zum Volltext (externe URL): Volltext

Abstract

Directed sets are a linear normed and partially ordered space in which the convex cone of all nonempty convex compact sets in |R is embedded. This space forms a Banach space and provides a visualization of differences of embedded convex compacts sets as usually non-convex sets in |R with attached normal directions. A. Rubinov suggested to define a subdifference for differences of convex functions via the difference of embedded convex subdifferentials. The directed subdifferential and its visualization, the Rubinov subdifferential, inherit interesting properties from the Banach space of directed sets, e.g. most of A. Ioffe's axioms for subdifferentials hold as well as the validness of the sum rule for differentials not as an inclusion, but in form of an equality. The relations to other known convex and non-convex subdifferentials are discussed as well as optimality conditions and the easy recovering of descent and ascent directions.

Weitere Angaben

Publikationsform: Preprint, Postprint
Zusätzliche Informationen: Contents:
1. Introduction
1.1 Basic Notations
2. Preliminaries - Some Known Subdifferentials
3. Directed Sets
4. The Directed Subdifferential
5. Optimally Conditions, Descent and Ascent Directions
6. Conclusions
Keywords: Nonsmooth analysis; Subdifferential calculus; Difference of convex (DC) functions; Optimality conditions; Ascent and descent directions
Fachklassifikationen: Mathematics Subject Classification Code: 49J52 (90C26 90C46 49J50)
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)
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 04 Mär 2021 09:53
Letzte Änderung: 25 Mai 2021 12:46
URI: https://eref.uni-bayreuth.de/id/eprint/63667