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, Volume 22, Issue 2, pp 716–738 | Cite as

Centers of sets with symmetry or cyclicity properties

  • Alberto SeegerEmail author
  • Mounir Torki
Original Paper

Abstract

We introduce an axiomatic formalism for the concept of the center of a set in a Euclidean space. Then we explain how to exploit possible symmetries and possible cyclicities in the set in order to localize its center. Special attention is paid to the determination of centers in cones of matrices. Despite its highly abstract flavor, our work has a strong connection with convex optimization theory. In fact, computing the so-called “incenter” of a solid closed convex cone is a matter of solving a nonsmooth convex optimization program. On the other hand, the concept of the incenter of a solid closed convex cone has a bearing on the complexity analysis and design of algorithms for convex optimization programs under conic constraints.

Keywords

Center of a set Symmetry space Cyclicity space Convex cone Cones of matrices Incenter and circumcenter Nonsmooth convex optimization 

Mathematics Subject Classification

15A48 47L07 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité d’AvignonAvignonFrance
  2. 2.CERIUniversité d’AvignonAvignonFrance

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