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The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II : Calculus

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Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II : Calculus.
In: Nonlinear Analysis : Theory, Methods & Applications. Bd. 75 (2012) Heft 3 . - S. 1058-1073.
ISSN 0362-546X
DOI: https://doi.org/10.1016/j.na.2011.04.073

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Abstract

We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina: The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definitions and examples, Nonlinear Anal., same volume]. Calculus rules for the directed subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the subdifferentials of Clarke, Dini, Michel-Penot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe's axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Zusätzliche Informationen: CONTENTS:
1. Introduction
2. Directed subdifferential of quasidifferentiable functions
2.1 Directed sets
2.2 Visualization of directed sets
2.3 Quasidifferentiable functions and the directed subdifferential
3. Calculus rules for the directed subdifferential for quasidifferentiable functions
4. Optimality conditions, descent and ascent directions
5. Connections to other subdifferentials
5.1 Relations between the directed subdifferential and other subdifferentials
5.2 Ioffe's axioms
6. Conclusions
Keywords: subdifferentials; quasidifferentiable functions; differences of sets; directed sets; directed subdifferential; Rubinov subdifferential
Fachklassifikationen: Mathematics Subject Classification Code: 49J52 (26B25 90C26)
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) > Lehrstuhl Mathematik V (Angewandte Mathematik) - Univ.-Prof. Dr. Lars Grüne
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
Eingestellt am: 22 Feb 2021 11:57
Letzte Änderung: 28 Mai 2021 10:12
URI: https://eref.uni-bayreuth.de/id/eprint/63242