Abstract The Douglas–Rachford algorithm is an optimization method that can be used for
solving feasibility problems. To apply the method, it is necessary that the problem at hand is …

The Douglas--Rachford algorithm is a classical and powerful splitting method for minimizing
the sum of two convex functions and, more generally, finding a zero of the sum of two …

We give properties of strict pseudocontractions and demicontractions defined on a Hilbert
space, which constitute wide classes of operators that arise in iterative methods for solving …

Abstract The Douglas–Rachford projection algorithm is an iterative method used to find a
point in the intersection of closed constraint sets. The algorithm has been experimentally …

Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating
averaged reflections algorithm, or relaxed Douglas--Rachford algorithm (DR λ), was first …

In this paper, we introduce and study a class of structured set-valued operators, which we
call union averaged nonexpansive. At each point in their domain, the value of such an …

This paper continues the study of general nonlinear transversality properties of collections of
sets and focuses on primal necessary (in some cases also sufficient) characterizations of the …

ABSTRACT The Douglas–Rachford (DR) algorithm is an iterative procedure that uses
sequential reflections onto convex sets and which has become popular for convex feasibility …

Different notions on regularity of sets and of collection of sets play an important role in the
analysis of the convergence of projection algorithms in nonconvex scenarios. While some …

We introduce a reformulation technique that converts a many-set feasibility problem into an
equivalent two-set problem. This technique involves reformulating the original feasibility …