Several acceleration schemes for solving the multiple-sets split feasibility problem
type: Item
instance of: scholarly article
title: Several acceleration schemes for solving the multiple-sets split feasibility problem
zbMATH Open document ID: 1261.65065
author: Jinling Zhaoa
author: Qingzhi Yang
published in: Linear Algebra and its Applications
publication date: 2012-08-27T00:00:00Z
reviewed by: Nicolae Popovici
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6072620
zbMATH Keywords: multiple-sets split feasibility problem
zbMATH Keywords: halfspace-relaxation
zbMATH Keywords: self-adaptive projection
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.laa.2012.05.018
OpenAlex ID: W1976215183
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DOI: 10.1016/J.LAA.2012.05.018
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review text: Let \(N, M, t\) and \(r\) be positive integers, let \(\{C_i \mid C_i \subseteq \mathbb{R}^N,\, i =1,\dots,t\}\) and \(\{Q_j \mid Q_j \subseteq \mathbb{R}^M,\, j =1,\dots,r\}\) be two families of nonempty closed convex sets, and let \(A\) be a real \((M \times N)\)-matrix. The multiple-sets split feasibility problem (MSFP) consists in finding a point \(x^\ast \in \cap_{i=1}^tC_i\) such that \(Ax^\ast \in \cap_{j=1}^rC_j\).NEWLINENEWLINEThe authors develop a self-adaptive algorithm for the numerical solution of the (MSFP) and prove its convergence. A special case of this algorithm as well as an accelerating relaxed algorithm are investigated. Numerical experiments are also provided.
description: scientific article; zbMATH DE number 6072620