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Mathematical Problems in Engineering
Volume 2018, Article ID 4123168, 7 pages
Research Article

The Split Feasibility Problem and Its Solution Algorithm

Institute of Operations Research, Qufu Normal University, Rizhao, Shandong 276826, China

Correspondence should be addressed to Biao Qu; moc.361@100oaibuq

Received 20 August 2017; Revised 7 November 2017; Accepted 5 December 2017; Published 8 January 2018

Academic Editor: Shuming Wang

Copyright © 2018 Biao Qu and Binghua Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.