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.