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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/328787 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849305071948398592 |
|---|---|
| author | Qiao-Li Dong Songnian He |
| author_facet | Qiao-Li Dong Songnian He |
| author_sort | Qiao-Li Dong |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-08e01180e5e94a21bcc69c8ecc7301d5 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-08e01180e5e94a21bcc69c8ecc7301d52025-08-20T03:55:33ZengWileyThe 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 |
| spellingShingle | Qiao-Li Dong Songnian He Modified Projection Algorithms for Solving the Split Equality Problems The Scientific World Journal |
| title | 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_short | Modified Projection Algorithms for Solving the Split Equality Problems |
| title_sort | modified projection algorithms for solving the split equality problems |
| url | http://dx.doi.org/10.1155/2014/328787 |
| work_keys_str_mv | AT qiaolidong modifiedprojectionalgorithmsforsolvingthesplitequalityproblems AT songnianhe modifiedprojectionalgorithmsforsolvingthesplitequalityproblems |