Survey: sixty years of Douglas–Rachford
SB Lindstrom, B Sims - Journal of the Australian Mathematical …, 2021 - cambridge.org
The Douglas–Rachford method is a splitting method frequently employed for finding zeros of
sums of maximally monotone operators. When the operators in question are normal cone …
sums of maximally monotone operators. When the operators in question are normal cone …
Adaptive Douglas--Rachford splitting algorithm for the sum of two operators
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 …
the sum of two convex functions and, more generally, finding a zero of the sum of two …
Linear convergence of the generalized Douglas–Rachford algorithm for feasibility problems
In this paper, we study the generalized Douglas–Rachford algorithm and its cyclic variants
which include many projection-type methods such as the classical Douglas–Rachford …
which include many projection-type methods such as the classical Douglas–Rachford …
A Lyapunov-type approach to convergence of the Douglas–Rachford algorithm for a nonconvex setting
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 …
point in the intersection of closed constraint sets. The algorithm has been experimentally …
Union averaged operators with applications to proximal algorithms for min-convex functions
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 …
call union averaged nonexpansive. At each point in their domain, the value of such an …
Convergence analysis under consistent error bounds
T Liu, BF Lourenço - Foundations of Computational Mathematics, 2024 - Springer
We introduce the notion of consistent error bound functions which provides a unifying
framework for error bounds for multiple convex sets. This framework goes beyond the …
framework for error bounds for multiple convex sets. This framework goes beyond the …
Primal necessary characterizations of transversality properties
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 …
sets and focuses on primal necessary (in some cases also sufficient) characterizations of the …
Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension
R Campoy - Set-Valued and Variational Analysis, 2023 - Springer
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 …
analysis of the convergence of projection algorithms in nonconvex scenarios. While some …
Constraint reduction reformulations for projection algorithms with applications to wavelet construction
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 …
equivalent two-set problem. This technique involves reformulating the original feasibility …
The Douglas–Rachford algorithm for a hyperplane and a doubleton
Abstract The Douglas–Rachford algorithm is a popular algorithm for solving both convex
and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent …
and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent …