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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005634
URN to cite this document: urn:nbn:de:bvb:703-epub-5634-8

Title data

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

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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.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erscheint in: Nonlinear Analysis : Theory, Methods & Applications. Bd. 75 (2012) Heft 3 . - S. 1058-1073 DOI: https://doi.org/10.1016/j.na.2011.04.073
Keywords:	subdifferentials; quasidifferentiable functions; differences of sets; directed sets; directed subdifferential; Rubinov subdifferential
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-5634-8
Date Deposited:	28 May 2021 10:11
Last Modified:	08 Jun 2021 08:06
URI:	https://epub.uni-bayreuth.de/id/eprint/5634

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