Conic optimization via operator splitting and homogeneous self-dual embedding
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 …
uses an operator splitting method, the alternating directions method of multipliers, to solve …
Linear convergence and metric selection for Douglas-Rachford splitting and ADMM
P Giselsson, S Boyd - IEEE Transactions on Automatic Control, 2016 - ieeexplore.ieee.org
Recently, several convergence rate results for Douglas-Rachford splitting and the
alternating direction method of multipliers (ADMM) have been presented in the literature. In …
alternating direction method of multipliers (ADMM) have been presented in the literature. In …
Distributed voltage control in distribution networks: Online and robust implementations
Voltage regulation in distribution networks is increasingly challenged by the penetration of
distributed energy resources (DERs). This paper develops a distributed voltage control …
distributed energy resources (DERs). This paper develops a distributed voltage control …
Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems
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 …
spaces. Of special interest are the method of alternating projections (AP) and the Douglas …
Convergence rates with inexact non-expansive operators
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 …
iteration built from non-expansive operators. The presented results include two main parts …
[HTML][HTML] The rate of linear convergence of the Douglas–Rachford algorithm for subspaces is the cosine of the Friedrichs angle
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 …
has found many applications. When specialized to two normal cone operators, it yields an …
Tight global linear convergence rate bounds for Douglas–Rachford splitting
P Giselsson - Journal of Fixed Point Theory and Applications, 2017 - Springer
Recently, several authors have shown local and global convergence rate results for Douglas–
Rachford splitting under strong monotonicity, Lipschitz continuity, and cocoercivity …
Rachford splitting under strong monotonicity, Lipschitz continuity, and cocoercivity …
Linear convergence of the Douglas–Rachford method for two closed sets
HM Phan - Optimization, 2016 - Taylor & Francis
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 …
nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the …
Alternating projections and Douglas-Rachford for sparse affine feasibility
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 …
underdetermined system of linear equations is an NP-complete problem that is typically …
Trajectory of alternating direction method of multipliers and adaptive acceleration
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 …
order optimisation methods in the literature owing to its simplicity, flexibility and efficiency …