Relaxed two points projection method for solving the multiple-sets split equality problem
type: Item
instance of: scholarly article
title: Relaxed two points projection method for solving the multiple-sets split equality problem
zbMATH Open document ID: 1391.49064
author: Yazheng Dang
author: Jian Yao
author: Yan Gao
published in: Numerical Algorithms
publication date: 2018-05-23T00:00:00Z
review text: Let \(H_1\), \(H_2\), \(H_3\) be real Hilbert spaces, \(C_i \subset H_1\), \(i=1,\dots,t\), \(Q_j \subset H_2\), \(j=1,\dots,r\) be closed convex sets, and \(A\in L(H_1, H_2)\), \(B\in L(H_2,H_3)\). The authors consider the problem of finding a point \(x\) such that \(x\in \cap_{i=1}^t C_i\), \(y\in \cap_{j=1}^r Q_j\) and \(Ax=By\). First, the original problem is transferred to an optimization problem. Next, the authors present a modified gradient projection algorithm to solve the problem and under suitable conditions establish the weak convergence of approximations to the solution. Numerical experiments are also discussed.
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65K15
zbMATH DE Number: 6871988
zbMATH Keywords: multiple-sets split equality problem
zbMATH Keywords: relaxed two points projection method
zbMATH Keywords: convergence
zbMATH Keywords: Hilbert space
MaRDI profile type: Publication
full work available at URL: s11075-017-0375-0
OpenAlex ID: W2738162455
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DOI: 10.1007/S11075-017-0375-0
description: scientific article; zbMATH DE number 6871988