The Douglas-Rachford algorithm in the affine-convex case
For researchers in convex optimization, this fills a gap in the convergence theory of the Douglas-Rachford algorithm under inconsistent constraints.
The paper provides convergence results for the Douglas-Rachford algorithm when one constraint is an affine subspace, extending previous results from halfspaces to general closed convex sets with least-squares solutions.
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.