Regularity of collections of sets and convergence of inexact alternating projections

TL;DR

This paper investigates how regularity properties of set collections influence the convergence of inexact alternating projection methods for feasibility problems, providing characterizations and convergence estimates.

Contribution

It introduces new characterizations of regularity properties and analyzes convergence in two inexact projection settings.

Findings

Regularity properties are characterized equivalently.

Convergence estimates are established for inexact projections.

The study enhances understanding of convergence behavior in feasibility algorithms.

Abstract

We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two settings of inexact alternating projections are considered and the corresponding convergence estimates are established and discussed.