Convergence and Perturbation Resilience of Dynamic String-Averaging Projection Methods

TL;DR

This paper studies the convergence and robustness of dynamic string-averaging projection methods for solving convex feasibility problems in Hilbert spaces, extending previous methods to include variable strings and weights.

Contribution

It introduces dynamic string-averaging projection methods with iteration-dependent strings and weights, and analyzes their convergence and perturbation resilience.

Findings

DSAP methods are convergent under new flexible conditions

DSAP methods exhibit bounded perturbation resilience

Potential application in superiorization heuristic for constrained optimization

Abstract

We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the scope of the family of SAP methods to allow iteration-index-dependent variable strings and weights and term such methods dynamic string-averaging projection (DSAP) methods. The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.