New hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem

In this paper, we propose two hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2023-03, Vol.38 (1), p.144-158
Main Authors: Dang, Ya-zheng, Wang, Long, Yang, Yao-heng
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Convergence
Feasibility
Hyperplanes
Iterative methods
Mathematics
Mathematics and Statistics
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Summary:In this paper, we propose two hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-023-4464-7