Modified alternating direction methods for the modified multiple-sets split feasibility problems
type: Item
instance of: scholarly article
title: Modified alternating direction methods for the modified multiple-sets split feasibility problems
zbMATH Open document ID: 1317.90286
author: Yuning Yang
author: Qingzhi Yang
author: Su Zhang
published in: Journal of Optimization Theory and Applications
publication date: 2014-11-03T00:00:00Z
review text: The authors present three modified alternative direction methods (ADMs) for solving two new multiple-sets split feasibility problem (MSFP) models. The first model is more separable than the original one, which enables one to apply a modified ADM with parallel feature to solve it. Then, to overcome the difficulty of computing projections onto the constraint sets, a special version of this modified method with the strategy of projections onto a half-space is given. The second model consists in finding a least Euclidean norm solution of the MSFP, for which another modified ADM is provided. Comparing it with some algorithms, the efficiency of these methods is shown in preliminary computational tests. These parallel methods are implemented in a personal computer without parallel-architecture. If the methods are implemented in a parallel computer, they may have a higher convergent speed.
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6363604
zbMATH Keywords: multiple-sets split feasibility problem
zbMATH Keywords: alternating direction method
zbMATH Keywords: parallel computing
zbMATH Keywords: half-space projection
reviewed by: Nada Djuranović-Miličić
MaRDI profile type: Publication
full work available at URL: s10957-013-0502-6
OpenAlex ID: W2085660764
cites work: The multiple-sets split feasibility problem and its applications for inverse problems
cites work: Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
cites work: Self-adaptive projection methods for the multiple-sets split feasibility problem
cites work: A self-adaptive projection method for solving the multiple-sets split feasibility problem
cites work: A self-adaptive projection-type method for nonlinear multiple-sets split feasibility problem
cites work: An efficient simultaneous method for the constrained multiple-sets split feasibility problem
cites work: A note on the CQ algorithm for the split feasibility problem
cites work: The relaxed CQ algorithm solving the split feasibility problem
cites work: A note on the alternating direction method of multipliers
cites work: Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming
cites work: An improved proximal alternating direction method for monotone variational inequalities with separable structure
cites work: A splitting method for separable convex programming
cites work: Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces
cites work: A new inexact alternating directions method for monotone variational inequalities
cites work: A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs
cites work: On the \(O(1/n)\) convergence rate of the Douglas-Rachford alternating direction method
cites work: Q3161693
cites work: Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization
DOI: 10.1007/S10957-013-0502-6
description: scientific article; zbMATH DE number 6363604