On farthest Bregman Voronoi cells. (3rd April 2022)

• Record Type: Journal Article
• Authors: Martínez-Legaz, Juan Enrique; Tamadoni Jahromi, Maryam; Naraghirad, Eskandar
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 937
• Page End: 947
• Publication Date: 2022-04-03
• Subjects: Voronoi cell -- Bregman distance -- farthest site; 52A20 -- 26B25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1915313
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Let g be a strictly convex function on an evenly convex set X ⊂ R n with nonempty interior. Assuming that g is differentiable on i n t X, we consider the Bregman distance D g associated with g . Given a set T ⊂ R n, whose elements are called sites, and a particular site s, the farthest g -Bregman Voronoi cell of s, denoted by F T g ( s ), consists of all points that are farther from s than from any other site with respect to D g . In this paper we study farthest g -Bregman Voronoi cells; in particular, we characterize those sets that can be written as F T g ( s ) for some T ⊂ R n and some s ∈ T .