Directed Derivatives of Convex Compact-Valued Mappings
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.
KeywordsDirected 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
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