Circumcentric directions of cones

Roger Behling, Yunier Bello-Cruz, Hugo Lara-Urdaneta, Harry Oviedo, Luiz Rafael Santos

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide inward directions to sets given by convex inequalities. In particular, we show that circumcentric directions of finitely generated cones belong to the interior of their polars. We also derive a measure of interiorness of the circumcentric direction, which then provides a special cone of search directions, all being feasible to the convex region under consideration.

Original languageEnglish
Pages (from-to)1069-1081
Number of pages13
JournalOptimization Letters
Issue number4
StatePublished - May 2023
Externally publishedYes


  • Circumcenter
  • Cone
  • Convex inequality
  • Feasible direction


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