English

The Douglas-Rachford algorithm in the affine-convex case

Optimization and Control 2020-04-14 v1 Numerical Analysis

Abstract

The Douglas-Rachford algorithm is a simple yet effective method for solving convex feasibility problems. However, if the underlying constraints are inconsistent, then the convergence theory is incomplete. We provide convergence results when one constraint is an affine subspace. As a consequence, we extend a result by Spingarn from halfspaces to general closed convex sets admitting least-squares solutions.

Keywords

Cite

@article{arxiv.1505.06408,
  title  = {The Douglas-Rachford algorithm in the affine-convex case},
  author = {Heinz H. Bauschke and Minh N. Dao and Walaa M. Moursi},
  journal= {arXiv preprint arXiv:1505.06408},
  year   = {2020}
}
R2 v1 2026-06-22T09:40:20.995Z