Convergence Properties of Dynamic String Averaging Projection Methods in the Presence of Perturbations

Abstract

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.

arXiv comment23 pages; accepted for publication in Numerical Algorithms

References in corpus (4)

• Perturbation Resilience and Superiorization of Iterative Algorithms
• Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods
• Convergence rate analysis for averaged fixed point iterations in the presence of Hölder regularity
• Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods

Cited by in corpus (5)

• Accelerating two projection methods via perturbations with application to Intensity-Modulated Radiation Therapy
• Superiorized Adaptive Projected Subgradient Method with Application to MIMO Detection
• String-Averaging Algorithms for Convex Feasibility with Infinitely Many Sets
• A string averaging method based on strictly quasi-nonexpansive operators with generalized relaxation
• Data-compatibility of algorithms