Modified Projection Algorithms for Solving the Split Equality Problems

Modified Projection Algorithms for Solving the Split Equality Problems

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively an...

Full description

Bibliographic Details
Main Authors: Qiao-Li Dong, Songnian He
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/328787
id doaj-08e01180e5e94a21bcc69c8ecc7301d5
record_format Article
spelling doaj-08e01180e5e94a21bcc69c8ecc7301d52020-11-25T03:27:13ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/328787328787Modified Projection Algorithms for Solving the Split Equality ProblemsQiao-Li Dong0Songnian He1College of Science, Civil Aviation University of China, Tianjin 300300, ChinaCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaThe split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.http://dx.doi.org/10.1155/2014/328787
collection DOAJ
language English
format Article
sources DOAJ
author Qiao-Li Dong
Songnian He
spellingShingle Qiao-Li Dong
Songnian He
Modified Projection Algorithms for Solving the Split Equality Problems
The Scientific World Journal
author_facet Qiao-Li Dong
Songnian He
author_sort Qiao-Li Dong
title Modified Projection Algorithms for Solving the Split Equality Problems
title_short Modified Projection Algorithms for Solving the Split Equality Problems
title_full Modified Projection Algorithms for Solving the Split Equality Problems
title_fullStr Modified Projection Algorithms for Solving the Split Equality Problems
title_full_unstemmed Modified Projection Algorithms for Solving the Split Equality Problems
title_sort modified projection algorithms for solving the split equality problems
publisher Hindawi Limited
series The Scientific World Journal
issn 2356-6140
1537-744X
publishDate 2014-01-01
description The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.
url http://dx.doi.org/10.1155/2014/328787
work_keys_str_mv AT qiaolidong modifiedprojectionalgorithmsforsolvingthesplitequalityproblems
AT songnianhe modifiedprojectionalgorithmsforsolvingthesplitequalityproblems
_version_ 1724588890419888128

Similar Items