相关论文: Eventual linear convergence of the Douglas Rachfor…
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for…
This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…
In this paper, we investigate the Douglas-Rachford method for two closed (possibly nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the Douglas-Rachford method converges locally with R-linear rate. In…
Douglas-Rachford method is a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Each of its iterations requires the sequential solution of two proximal subproblems. The aim of this work is to present a…
The Douglas-Rachford splitting algorithm is a classical optimization method that has found many applications. When specialized to two normal cone operators, it yields an algorithm for finding a point in the intersection of two convex sets.…
In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
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 algorithm and the alternating projection algorithm. Specifically,…
The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one…
The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze…
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 maximally monotone operators. Although this algorithm is well…
We analyze the Douglas-Rachford splitting method for weakly convex optimization problems, by the token of the Douglas-Rachford envelope, a merit function akin to the Moreau envelope. First, we use epi-convergence techniques to show that…
We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope…
The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility…
In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…