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Directed Derivatives of Convex Compact-Valued Mappings

  • Robert Baier
  • Elza M. Farkhi
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 54)

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.

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 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Robert Baier
    • 1
  • Elza M. Farkhi
    • 2
  1. 1.Chair of Applied MathematicsUniversity of BayreuthBayreuthGermany
  2. 2.School of Mathematical Sciences Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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