Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings

• 成果类型: Article
• 署名作者: Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
• 署名单位: University of British Columbia
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0659-7
• 发表日期: 2013
• 页码: 55-70
• 关键词: proximal average; algorithm; Duality

摘要

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly nonexpansive mappings is nearly equal to the average of the ranges of the mappings. A striking application of this result yields that the average of asymptotically regular firmly nonexpansive mappings is also asymptotically regular. Throughout, examples are provided to illustrate the theory. We also obtain detailed information on the domain and range of the resolvent average.