The Cyclic Douglas-Rachford Method for Inconsistent Feasibility Problems

TL;DR

This paper analyzes the cyclic Douglas-Rachford algorithm's behavior when applied to inconsistent convex feasibility problems, where the intersection may be empty, providing insights into its convergence properties.

Contribution

It introduces a detailed analysis of the cyclic Douglas-Rachford method for inconsistent problems, expanding understanding beyond feasible cases.

Findings

Provides convergence analysis for inconsistent cases

Characterizes the behavior of the algorithm when the intersection is empty

Offers theoretical insights into the algorithm's dynamics

Abstract

We analyse the behaviour of the newly introduced cyclic Douglas-Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty.