Related papers: On the behaviour of the Douglas-Rachford algorithm…
Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating…
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 and Peaceman-Rachford algorithms have been successfully employed to solve convex optimization problems, or more generally find zeros of monotone inclusions. Recently, the behaviour of these methods in the inconsistent…
We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…
The problem of finding a zero of the sum of two maximally monotone operators is of central importance in optimization. One successful method to find such a zero is the Douglas-Rachford algorithm which iterates a firmly nonexpansive operator…
In this paper, we study a parameterized Douglas-Rachford splitting method for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized…
In this paper we study new algorithmic structures with Douglas- Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and into…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
We provide a simple analysis of the Douglas-Rachford splitting algorithm in the context of $\ell^1$ minimization with linear constraints, and quantify the asymptotic linear convergence rate in terms of principal angles between relevant…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
Douglas-Rachford method is a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Weak convergence in this method to a solution of the underlying monotone inclusion problem in the general case remained an…
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 case, the general nonconvex inconsistent case is far from being…
In this work we focus on the convex feasibility problem (CFP) in Hilbert space. A specific method in this area that has gained a lot of interest in recent years is the Douglas-Rachford (DR) algorithm. This algorithm was originally…
The proximal point algorithm (PPA) is the most widely recognized method for solving inclusion problems and serves as the foundation for many numerical algorithms. Despite this popularity, its convergence results have been largely limited to…
The primal-dual Douglas-Rachford method is a well-known algorithm to solve optimization problems written as convex-concave saddle-point problems. Each iteration involves solving a linear system involving a linear operator and its adjoint.…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
The basic optimization problem of road design is quite challenging due to a objective function that is the sum of nonsmooth functions and the presence of set constraints. In this paper, we model and solve this problem by employing the…
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization problems. In order to successfully use the method, it is…
We study the convergence of the adaptive Douglas--Rachford (aDR) algorithm for solving a multioperator inclusion problem involving the sum of maximally comonotone operators. To address such problems, we adopt a product space reformulation…