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Directed Sets and Differences of Convex Compact Sets

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005452
URN to cite this document: urn:nbn:de:bvb:703-epub-5452-7

Title data

Baier, Robert ; Farkhi, Elza:
Directed Sets and Differences of Convex Compact Sets.
Bayreuth , 1999

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Abstract

This paper is devoted to directed sets and differences of convex compact sets. The authors use the specific parametrization of convex compact sets via their support functions and consider the supporting faces as lower-dimensional convex sets. Extending this approach they define a directed set as a pair of mappings that associate to each unit direction an (n-1)-dimensional directed set and a scalar function determining the position of this face in |R^n. The main differences of the authors' approach to other existing embeddings are that there are no equivalence classes and, secondly, that differences of directed convex sets in |R^n are not real-valued functions of n arguments. The authors provide an application, by giving an example of set-valued interpolation where nonconvex visualizations of directed sets appear as results.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen In:
Polis, Michael P. ; Dontchev, Asen L. ; Kall, Peter ; Lasiecka, Irena ; Olbrot, Andrzej W. (Hrsg.): Systems modelling and optimization : Proceedings of the 18th IFIP TC7 Conference held in Detroit, Michigan, July 22-25, 1997. - Boca Raton : Chapman & Hall , 1999 . - S. 135-143
Keywords: convex sets in n dimensions; set-valued maps; set-valued interpolation; interval arithmetic; set-valued analysis
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-5452-7
Date Deposited: 06 May 2021 11:22
Last Modified: 06 May 2021 11:22
URI: https://epub.uni-bayreuth.de/id/eprint/5452

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