Convergence properties of dynamic string-averaging projection methods in the presence of perturbations

被引：0
作者：
Christian Bargetz
Simeon Reich
Rafał Zalas
机构：
[1] The Technion—Israel Institute of Technology,Department of Mathematics
[2] University of Innsbruck,Department of Mathematics
来源：
Numerical Algorithms | 2018年 / 77卷
关键词：
Linear rate; Perturbation resilience; String averaging; Superiorization; 46N10; 46N40; 47H09; 47H10; 47J25; 47N10; 65F10; 65J99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Assuming that the absence of perturbations guarantees weak or strong convergence to a common fixed point, we study the behavior of perturbed products of an infinite family of nonexpansive operators. Our main result indicates that the convergence rate of unperturbed products is essentially preserved in the presence of perturbations. This, in particular, applies to the linear convergence rate of dynamic string-averaging projection methods, which we establish here as well. Moreover, we show how this result can be applied to the superiorization methodology.
引用
收藏
页码：185 / 209
页数：24
相关论文
共 72 条
  • [1] Aleyner A(2008)Block-iterative algorithms for solving convex feasibility problems in Hilbert and in Banach spaces J. Math. Anal. Appl. 343 427-435
  • [2] Reich S(1950)Theory of reproducing kernels Trans. Amer. Math. Soc. 68 337-404
  • [3] Aronszajn N(2011)The rate of convergence in the method of alternating projections Algebra i Analiz 23 1-30
  • [4] Badea C(1996)On projection algorithms for solving convex feasibility problems SIAM Rev. 38 367-426
  • [5] Grivaux S(2015)Linear and strong convergence of algorithms involving averaged nonexpansive operators J. Math. Anal. Appl. 421 1-20
  • [6] Müller V(2003)Convergence rate analysis and error bounds for projection algorithms in convex feasibility problems Optim. Methods Softw. 18 377-394
  • [7] Bauschke HH(2017)Convergence rate analysis for averaged fixed point iterations in common fixed point problems SIAM J. Optim. 27 1-33
  • [8] Borwein JM(2007)Stable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problems IEEE J. Selected Topics Signal Process. 1 540-547
  • [9] Bauschke HH(2008)Stable convergence theorems for infinite products and powers of nonexpansive mappings Numer. Funct. Anal. Optim. 29 304-323
  • [10] Noll D(2014)Properties of a class of approximately shrinking operators and their applications Fixed Point Theory 15 399-426
12345678