Iterating Bregman retractions

被引：20

作者：

Bauschke, HH ^{[1
]}

Combettes, AL

机构：

[1] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

[2] Univ Paris 06, Lab Jacques Louis Lions, F-75005 Paris 6, France

来源：

SIAM JOURNAL ON OPTIMIZATION | 2003年 / 13卷 / 04期

关键词：

backward Bregman projection; Bregman distance; Bregman function; Bregman projection; Bregman retraction; convex feasibility problem; forward Bregman projection; Legendre function; paracontraction; projection algorithm;

D O I：

10.1137/S1052623402410557

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The notion of a Bregman retraction of a closed convex set in Euclidean space is introduced. Bregman retractions include backward Bregman projections and forward Bregman projections, as well as their convex combinations, and are thus quite flexible. The main result on iterating Bregman retractions unifies several convergence results on projection methods for solving convex feasibility problems. It is also used to construct new sequential and parallel algorithms.

引用

页码：1159 / 1173

页数：15

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