Tight global linear convergence rate bounds for Douglas-Rachford splitting
type: Item
instance of: scholarly article
title: Tight global linear convergence rate bounds for Douglas-Rachford splitting
zbMATH Open document ID: 1380.65104
author: Pontus Giselsson
published in: Journal of Fixed Point Theory and Applications
publication date: 2017-12-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1506.01556
review text: The paper establishes linear convergence rate bounds for Douglas-Rachford splitting for monotone inclusion problems with three sets of assumptions. In the first case, one operator is assumed to be strongly monotone and the other is cocoercive. In the second case, one operator is assumed to be both strongly monotone and Lipschitz continuous. In the third case, one operator is assumed to be both strongly monotone and cocoercive. All rate bounds are shown to be tight.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 6817744
zbMATH Keywords: Douglas-Rachford splitting
zbMATH Keywords: linear convergence
zbMATH Keywords: monotone operators
zbMATH Keywords: fixed-point iterations
zbMATH Keywords: monotone inclusion problems
describes a project that uses: UNLocBoX
MaRDI profile type: Publication
OpenAlex ID: W2962964459
Wikidata QID: Q59612021
arXiv ID: 1506.01556
cites work: The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle
cites work: Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces
cites work: Convex analysis and monotone operator theory in Hilbert spaces
cites work: Local Linear Convergence of the Alternating Direction Method of Multipliers on Quadratic or Linear Programs
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: Proximal Splitting Methods in Signal Processing
cites work: Compositions and convex combinations of averaged nonexpansive operators
cites work: Faster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions
cites work: Convergence Rate Analysis of Several Splitting Schemes
cites work: Eventual linear convergence of the Douglas-Rachford iteration for basis pursuit
cites work: On the global and linear convergence of the generalized alternating direction method of multipliers
cites work: On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
cites work: Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
cites work: A dual algorithm for the solution of nonlinear variational problems via finite element approximation
cites work: Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems
cites work: Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM
cites work: On the \(O(1/n)\) convergence rate of the Douglas-Rachford alternating direction method
cites work: Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
cites work: On the linear convergence of the alternating direction method of multipliers
cites work: Explicit Convergence Rate of a Distributed Alternating Direction Method of Multipliers
cites work: Q5847510
cites work: Splitting Algorithms for the Sum of Two Nonlinear Operators
cites work: Mean Value Methods in Iteration
cites work: Monotone (nonlinear) operators in Hilbert space
cites work: The Numerical Solution of Parabolic and Elliptic Differential Equations
cites work: Linear convergence of the Douglas–Rachford method for two closed sets
cites work: On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
DOI: 10.1007/S11784-017-0417-1
description: scientific article