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

Title data

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

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Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: 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
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 11:57
Last Modified: 28 May 2021 10:12
URI: https://eref.uni-bayreuth.de/id/eprint/63242