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Directed Derivatives of Convex Compact-Valued Mappings

Titelangaben

Baier, Robert ; Farkhi, Elza M.:
Directed Derivatives of Convex Compact-Valued Mappings.
In: Hadjisavvas, Nicolas ; Pardalos, Panos M. (Hrsg.): Advances in Convex Analysis and Global Optimization : honoring the memory of C. Caratheodory (1873 - 1950). - Dordrecht : Kluwer Academic Publishers , 2001 . - S. 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

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.

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Publikationsform: Aufsatz in einem Buch
Begutachteter Beitrag: Ja
Zusätzliche Informationen: 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
Fachklassifikationen: Mathematics Subject Classification Code: 26E25 (52A20 58C25 46G05 54C60 41A45)
Institutionen der Universität: 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
500 Naturwissenschaften und Mathematik > 500 Naturwissenschaften
500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 23 Feb 2021 08:21
Letzte Änderung: 11 Mai 2021 11:01
URI: https://eref.uni-bayreuth.de/id/eprint/63316