On the finite convergence of the Douglas-Rachford algorithm for solving (not necessarily convex) feasibility problems in Euclidean spaces

TL;DR

This paper establishes new conditions under which the Douglas-Rachford algorithm finitely converges when solving feasibility problems in Euclidean spaces, supported by numerous illustrative examples.

Contribution

It introduces novel sufficient conditions for finite convergence of the Douglas-Rachford algorithm in non-convex feasibility problems.

Findings

New sufficient conditions for finite convergence

Numerous examples illustrating the results

Applicability to non-convex feasibility problems

Abstract

Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerous examples illustrate our results.