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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005633
URN to cite this document: urn:nbn:de:bvb:703-epub-5633-2

Title data

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I : Definition and examples.
Bayreuth , 2011

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Abstract

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.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erscheint in: Nonlinear Analysis : Theory, Methods & Applications. Bd. 75 (2012) Heft 3 . - S. 1074-1088 DOI: https://doi.org/10.1016/j.na.2011.04.074
Keywords:	Subdifferentials; Quasidifferentiable functions; Differences of sets; Directed sets; Directed subdifferential; Amenable and lower-,Cᵏ,functions
DDC Subjects:	500 Science 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-5633-2
Date Deposited:	28 May 2021 10:06
Last Modified:	08 Jun 2021 08:05
URI:	https://epub.uni-bayreuth.de/id/eprint/5633

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