The Split Feasibility Problem and Its Solution Algorithm
The split feasibility problem arises in many fields in the real world, such as signal processing, image reconstruction, and medical care. In this paper, we present a solution algorithm called memory gradient projection method for solving the split feasibility problem, which employs a parameter and t...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2018-01-01
|
Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2018/4123168 |
id |
doaj-2f69ec6362744ef5bafdb3602a2208a0 |
---|---|
record_format |
Article |
spelling |
doaj-2f69ec6362744ef5bafdb3602a2208a02020-11-24T21:47:51ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/41231684123168The Split Feasibility Problem and Its Solution AlgorithmBiao Qu0Binghua Liu1Institute of Operations Research, Qufu Normal University, Rizhao, Shandong 276826, ChinaInstitute of Operations Research, Qufu Normal University, Rizhao, Shandong 276826, ChinaThe split feasibility problem arises in many fields in the real world, such as signal processing, image reconstruction, and medical care. In this paper, we present a solution algorithm called memory gradient projection method for solving the split feasibility problem, which employs a parameter and two previous iterations to get the next iteration, and its step size can be calculated directly. It not only improves the flexibility of the algorithm, but also avoids computing the largest eigenvalue of the related matrix or estimating the Lipschitz constant in each iteration. Theoretical convergence results are established under some suitable conditions.http://dx.doi.org/10.1155/2018/4123168 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Biao Qu Binghua Liu |
spellingShingle |
Biao Qu Binghua Liu The Split Feasibility Problem and Its Solution Algorithm Mathematical Problems in Engineering |
author_facet |
Biao Qu Binghua Liu |
author_sort |
Biao Qu |
title |
The Split Feasibility Problem and Its Solution Algorithm |
title_short |
The Split Feasibility Problem and Its Solution Algorithm |
title_full |
The Split Feasibility Problem and Its Solution Algorithm |
title_fullStr |
The Split Feasibility Problem and Its Solution Algorithm |
title_full_unstemmed |
The Split Feasibility Problem and Its Solution Algorithm |
title_sort |
split feasibility problem and its solution algorithm |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2018-01-01 |
description |
The split feasibility problem arises in many fields in the real world, such as signal processing, image reconstruction, and medical care. In this paper, we present a solution algorithm called memory gradient projection method for solving the split feasibility problem, which employs a parameter and two previous iterations to get the next iteration, and its step size can be calculated directly. It not only improves the flexibility of the algorithm, but also avoids computing the largest eigenvalue of the related matrix or estimating the Lipschitz constant in each iteration. Theoretical convergence results are established under some suitable conditions. |
url |
http://dx.doi.org/10.1155/2018/4123168 |
work_keys_str_mv |
AT biaoqu thesplitfeasibilityproblemanditssolutionalgorithm AT binghualiu thesplitfeasibilityproblemanditssolutionalgorithm AT biaoqu splitfeasibilityproblemanditssolutionalgorithm AT binghualiu splitfeasibilityproblemanditssolutionalgorithm |
_version_ |
1725895155360202752 |