Cyclic Relaxed Douglas-Rachford Splitting for Inconsistent Nonconvex Feasibility
Optimization and Control
2026-05-06 v1
Abstract
We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by Borwein and Tam [2014] and the classical cyclic projections algorithm. We characterize the fixed points of the cyclic relaxed Douglas-Rachford algorithm and show the relation of the {\em shadows} of these fixed points to the fixed points of the cyclic projections algorithm. Finally, we provide conditions that guarantee local quantitative convergence estimates in the nonconvex, inconsistent setting.
Cite
@article{arxiv.2502.12285,
title = {Cyclic Relaxed Douglas-Rachford Splitting for Inconsistent Nonconvex Feasibility},
author = {Thi Lan Dinh and G. S. Matthijs Jansen and D. Russell Luke},
journal= {arXiv preprint arXiv:2502.12285},
year = {2026}
}
Comments
31 pages, no figures, 21 references