An iterative algorithm for the split equality and multiple-sets split equality problem
type: Item
instance of: scholarly article
title: An iterative algorithm for the split equality and multiple-sets split equality problem
zbMATH Open document ID: 1474.65176
DOI: 10.1155/2014/620813
author: Yujing Wu
author: Luoyi Shi
author: Rudong Chen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The multiple-sets split equality problem (MSSEP) requires finding a point \(x \in \cap_{i = 1}^N C_i\), \(y \in \cap_{j = 1}^M Q_j\) such that \(A x = B y\), where \(N\) and \(M\) are positive integers, \(\{C_1, C_2, \ldots, C_N \}\) and \(\{Q_1, Q_2, \ldots, Q_M \}\) are closed convex subsets of Hilbert spaces \(H_1\), \(H_2\), respectively, and \(A : H_1 \rightarrow H_3\), \(B : H_2 \rightarrow H_3\) are two bounded linear operators. When \(N = M = 1\), the MSSEP is called the split equality problem (SEP). If \(B = I\), then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 7022741
Wikidata QID: Q59040039
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/620813
OpenAlex ID: W2069122684
cites work: A multiprojection algorithm using Bregman projections in a product space
cites work: The multiple-sets split feasibility problem and its applications for inverse problems
cites work: Iterative oblique projection onto convex sets and the split feasibility problem
cites work: A unified treatment of some iterative algorithms in signal processing and image reconstruction
cites work: A note on the CQ algorithm for the split feasibility problem
cites work: A variable Krasnosel'skii–Mann algorithm and the multiple-set split feasibility problem
cites work: The relaxed CQ algorithm solving the split feasibility problem
cites work: Generalized KM theorems and their applications
cites work: A relaxed alternating CQ-algorithm for convex feasibility problems
cites work: Strong convergence of iterative algorithms for the split equality problem
cites work: Q3998720
cites work: Q3322631
cites work: An iterative regularization method for the solution of the split feasibility problem in Banach spaces
description: scientific article; zbMATH DE number 7022741