Iterative method for solving the linear feasibility problem
type: Item
instance of: scholarly article
title: Iterative method for solving the linear feasibility problem
zbMATH Open document ID: 1165.90010
author: R. Dudek
published in: Journal of Optimization Theory and Applications
publication date: 2008-09-23T00:00:00Z
review text: Consider the linear feasibility problem of finding a solution \(x^*\) of a consistent system of linear inequalities \(G^Tx\leq b,\) where \(G\) is a matrix of size \(n\times m\) with columns \( g_{i}\in \mathbb R^n\), \(i\in I=\{ 1,\dots ,m\}\), \(x=(x_1,x_2\dots,x_n)^T\in \mathbb R^n\), \(b=(b_1,b_2,\dots ,b_m)^T\in \mathbb R^m\). Some solution methods use relaxed, averaged projections and other invoke surrogate constraints as for example Yang-Murty' method [\textit{K. Yang} and \textit{K. G. Murty}, J. Optim. Theory Appl. 72, 163--185 (1992; Zbl 0793.90035)]. In this paper the author proposes (Iterative Scheme 2.1) a blend of these two approaches. The author compares the computation results of his method with the surrogate constraint method of Yang-Murty and points out the advantage of his method.
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C57
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 5346077
zbMATH Keywords: surrogate constraints
zbMATH Keywords: metric projections
reviewed by: I. M. Stancu-Minasian
MaRDI profile type: Publication
full work available at URL: s10957-007-9163-7
OpenAlex ID: W1980382020
cites work: A class of optimized row projection methods for solving large nonsymmetric linear systems
cites work: Q4091727
cites work: Relaxed outer projections, weighted averages and convex feasibility
cites work: A simultaneous projections method for linear inequalities
cites work: New iterative methods for linear inequalities
cites work: The method of projections for finding the common point of convex sets
DOI: 10.1007/S10957-007-9163-7
description: scientific article; zbMATH DE number 5346077