A Cyclic Douglas-Rachford Iteration Scheme

TL;DR

This paper introduces two new Douglas-Rachford inspired algorithms for solving N-set convex feasibility problems in Hilbert spaces, demonstrating weak convergence and promising numerical results compared to classical methods.

Contribution

The paper proposes novel Douglas-Rachford based iteration schemes for N-set convex feasibility problems with proven convergence properties.

Findings

Weak convergence to a common projection point

Norm convergence for affine subspaces

Promising numerical performance compared to classical methods

Abstract

In this paper we present two Douglas-Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas-Rachford scheme, are promising.