We introduce a first-order method for solving very large convex cone programs. The method
uses an operator splitting method, the alternating directions method of multipliers, to solve …

Recently, several convergence rate results for Douglas-Rachford splitting and the
alternating direction method of multipliers (ADMM) have been presented in the literature. In …

Voltage regulation in distribution networks is increasingly challenged by the penetration of
distributed energy resources (DERs). This paper develops a distributed voltage control …

We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean
spaces. Of special interest are the method of alternating projections (AP) and the Douglas …

In this paper, we present a convergence rate analysis for the inexact Krasnosel'skiĭ–Mann
iteration built from non-expansive operators. The presented results include two main parts …

Abstract 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 …

Recently, several authors have shown local and global convergence rate results for Douglas–
Rachford splitting under strong monotonicity, Lipschitz continuity, and cocoercivity …

In this paper, we investigate the Douglas–Rachford method (DR) for two closed (possibly
nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the …

The problem of finding a vector with the fewest nonzero elements that satisfies an
underdetermined system of linear equations is an NP-complete problem that is typically …

The alternating direction method of multipliers (ADMM) is one of the most widely used first-
order optimisation methods in the literature owing to its simplicity, flexibility and efficiency …