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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 zum Zitieren der Version auf EPub Bayreuth: urn:nbn:de:bvb:703-epub-5633-2

Titelangaben

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.

Weitere Angaben

Publikationsform: Preprint, Postprint
Zusätzliche Informationen (öffentlich sichtbar): 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
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Sprache: Englisch
Titel an der UBT entstanden: Ja
URN: urn:nbn:de:bvb:703-epub-5633-2
Eingestellt am: 28 Mai 2021 10:06
Letzte Änderung: 08 Jun 2021 08:05
URI: https://epub.uni-bayreuth.de/id/eprint/5633

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