Linear Convergence of Projection Algorithms

TL;DR

This paper investigates the conditions under which projection algorithms for solving systems of closed sets exhibit linear convergence, enhancing understanding of their efficiency and reliability in feasibility problems.

Contribution

It provides new theoretical results on the linear convergence of various projection algorithms, complementing existing research in the field.

Findings

Established conditions for linear convergence of projection algorithms.

Extended current understanding of convergence behavior in feasibility problems.

Contributed to the theoretical foundation of projection methods.

Abstract

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we study linear convergence of several projection algorithms for systems of finitely many closed sets. The results complement contemporary research on the same topic.