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The Directed Subdifferential of DC functions

Title data

Baier, Robert ; Farkhi, Elza:
The Directed Subdifferential of DC functions.
Bonn , 2008 . - 19 p.

Official URL: Volltext

Abstract in another language

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.

Further data

Item Type: Preprint, postprint
Additional notes: 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
Subject classification: Mathematics Subject Classification Code: 49J52 (90C26 90C46 49J50)
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)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 04 Mar 2021 09:53
Last Modified: 25 May 2021 12:46