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arXiv · 2502.12285

Cyclic Relaxed Douglas-Rachford Splitting for Inconsistent Nonconvex Feasibility

Thi Lan Dinh·G. S. Matthijs Jansen·D. Russell Luke
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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.

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Thi Lan Dinh, G. S. Matthijs Jansen, D. Russell Luke. 2025-02-17. Cyclic Relaxed Douglas-Rachford Splitting for Inconsistent Nonconvex Feasibility. https://doi.org/10.1007/s10957-026-02996-2

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