The Split Feasibility Problem and Its Solution Algorithm

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...

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Main Authors: Biao Qu, Binghua Liu
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
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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
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AT biaoqu splitfeasibilityproblemanditssolutionalgorithm
AT binghualiu splitfeasibilityproblemanditssolutionalgorithm
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