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The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I : Definition and examples

Title data

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I : Definition and examples.
In: Nonlinear Analysis : Theory, Methods & Applications. Vol. 75 (2012) Issue 3 . - pp. 1074-1088.
ISSN 0362-546X
DOI: https://doi.org/10.1016/j.na.2011.04.074

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Abstract in another language

We extend the definition of the directed subdifferential, originally introduced in [R. Baier, E. Farkhi: The directed subdifferential of DC functions, in: A. Leizarowitz, B. S. Mordukhovich, I. Shafrir, A. J. Zaslavski (Eds.), Nonlinear Analysis and Optimization II: Optimization. A Conference in Celebration of Alex Ioffe's 70th and Simeon Reich's 60th Birthdays, June 18-24, 2008, Haifa, Israel, in: AMS Contemp. Mathem. 513, AMS and Bar-Ilan University, 2010, pp. 27-43], for differences of convex functions (DC) to the wider class of quasidifferentiable functions. Such generalization efficiently captures differential properties of a wide class of functions including amenable and lower/upper-Ck functions. While preserving the most important properties of the quasidifferential, such as exact calculus rules, the directed subdifferential lacks the major drawbacks of quasidifferential: non-uniqueness and “inflation in size” of the two convex sets representing the quasidifferential after applying calculus rules. The Rubinov subdifferential is defined as the visualization of the directed subdifferential.

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Item Type: Article in a journal
Refereed: Yes
Additional notes: CONTENTS:
1. Introduction
2. Preliminaries
3. Quasidifferentiable functions
3.1 Definition and some basic properties
3.2 Examples
4. Directed sets and the directed subdifferential
4.1 Directed sets
4.2 The directed and Rubinov subdifferentials
5. Directed subdifferential for lower-<i>C<sup>k</sup></i> and amenable functions
6. Conclusions
Keywords: Subdifferentials; Quasidifferentiable functions; Differences of sets; Directed sets; Directed subdifferential; Amenable and lower-,Cᵏ,functions
Subject classification: Mathematics Subject Classification Code: 49J52 (26B25 90C26)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
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
Date Deposited: 22 Feb 2021 11:52
Last Modified: 28 May 2021 10:07
URI: https://eref.uni-bayreuth.de/id/eprint/63238