On the local convergence of the Douglas-Rachford algorithm

被引：32
作者：
Bauschke, H. H. [1 ]
Noll, D. [2 ]
机构：
[1] Univ British Columbia, Kelowna, BC, Canada
[2] Inst Math Toulouse, Toulouse, France
来源：
ARCHIV DER MATHEMATIK | 2014年 / 102卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Nonconvex feasibility problem; Fixed-point; Discrete dynamical system; Convergence; Stability;
D O I：
10.1007/s00013-014-0652-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss the Douglas-Rachford algorithm to solve the feasibility problem for two closed sets A,B in . We prove its local convergence to a fixed point when A,B are finite unions of convex sets. We also show that for more general nonconvex sets the scheme may fail to converge and start to cycle, and may then even fail to solve the feasibility problem.
引用
收藏
页码：589 / 600
页数：12
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