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Directed Derivatives of Convex Compact-Valued Mappings

Title data

Baier, Robert ; Farkhi, Elza M.:
Directed Derivatives of Convex Compact-Valued Mappings.
In: Hadjisavvas, Nicolas ; Pardalos, Panos M. (ed.): Advances in Convex Analysis and Global Optimization : honoring the memory of C. Caratheodory (1873 - 1950). - Dordrecht : Kluwer Academic Publishers , 2001 . - pp. 501-514 . - (Nonconvex Optimization and its Applications ; 54 )
ISBN 978-0-7923-6942-4
DOI: https://doi.org/10.1007/978-1-4613-0279-7_32

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Abstract in another language

Convex compact sets can be embedded into the Banach space of directed sets. Directed sets allow a visualization as possibly non-convex, compact sets in |R^n and hence, this space could be used to visualize differences of embedded convex compact sets. The main application is the visualization as well as the theoretical and numerical calculation of set-valued derivatives. Known notions of affine, semi-affine and quasi-affine maps and their derivatives are studied.

Further data

Item Type: Article in a book
Refereed: Yes
Additional notes: Contents:
1. Introduction
2. Directed Sets
3. Derivatives of Set-Valued Mappings
4. Examples of Directed Derivatives
5. Summary
Keywords: Directed sets; Set-valued derivatives; Differences of convex sets and their visualization; Affine, semi-affine, quasi-affine maps; Embedding of convex compact sets into a vector space; Directed intervals
Subject classification: Mathematics Subject Classification Code: 26E25 (52A20 58C25 46G05 54C60 41A45)
Institutions of the University: 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
500 Science > 500 Natural sciences
500 Science > 510 Mathematics
Date Deposited: 23 Feb 2021 08:21
Last Modified: 11 May 2021 11:01
URI: https://eref.uni-bayreuth.de/id/eprint/63316