Circumcentric directions of cones

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 partic...

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Bibliographic Details
Published inarXiv.org
Main Authors Behling, Roger, Bello-Cruz, Yunier, Lara-Urdaneta, Hugo, Oviedo, Harry, Luiz-Rafael Santos
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.07.2022
Subjects
Cones
Feasibility
Mathematics - Optimization and Control
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2112.08314