Tight coefficients of averaged operators via scaled relative graph

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:490

Article

Huang, Xinmeng¹  Rya, Ernest K.²  Yin, Wotao³ 

[1] Univ Sci & Technol China, Sch Math Sci, Hefei, Peoples R China

[2] Seoul Natl Univ, Dept Math Sci, Seoul, South Korea

[3] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA

关键词: Averaged operator;    Composition of operators;    Nonexpansive operator;    Euclidean geometry;    Three operators;   

DOI  :  10.1016/j.jmaa.2020.124211

来源: Elsevier

【 摘 要 】

Many iterative methods in optimization are fixed-point iterations with averaged operators. As such methods converge at an O(1/k) rate with the constant determined by the averagedness coefficient, establishing small averagedness coefficients for operators is of broad interest. In this paper, we show that the averagedness coefficients of the composition of averaged operators by Ogura and Yamada (2002) [21] and the three-operator splitting by Davis and Yin (2017) [9] are tight. The analysis relies on the scaled relative graph, a geometric tool recently proposed by Ryu et al. (2019) [25]. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free