An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms
type: Item
instance of: scholarly article
title: An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms
zbMATH Open document ID: 1056.65027
author: N. Echebest
author: M. T. Guardarucci
author: M. C. Vacchino
author: H. Scolnik
published in: Numerical Algorithms
publication date: 2004-08-10T00:00:00Z
review text: An accelerated iterative projection method is presented for solving systems of linear inequalities. This method is an extension of the projection methods for solving systems of linear equations given by \textit{H. Scolnik, N. Echebest, M. T. Guardarucci}, and \textit{M. C. Vacchino} [Stud. Comput. Math. 8, 457--471 (2001; Zbl 1003.65027); Ann. Oper. Res. 117, 95--115 (2002; Zbl 1023.65026)]. The general scheme is similar to the incomplete projection algorithm, and therefore it is very convenient for parallel processing. The idea is that at the current iterate the set of violated constraints is splitted into subsets or blocks, in such a way that the required incomplete projection is obtained by combining exact projection onto simple convex sets. The new iterate is defined by the projection of the current iterate onto a separating hyperplane. The advantages of this approach are illustrated both theoretically and numerically.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 2085901
zbMATH Keywords: aggregated projection methods
zbMATH Keywords: convergence acceleration
zbMATH Keywords: parallel computation
zbMATH Keywords: numerical examples
zbMATH Keywords: systems of linear inequalities
zbMATH Keywords: incomplete projection algorithm
reviewed by: Liu Xinguo
describes a project that uses: SPARSKIT
MaRDI profile type: Publication
full work available at URL: b:numa.0000021777.31773.c3
OpenAlex ID: W2032138022
DOI: 10.1023/B:NUMA.0000021777.31773.C3
description: scientific article; zbMATH DE number 2085901