Alternating iterative algorithms for the split equality problem without prior knowledge of operator norms

In this paper, we study the alternating CQ algorithm for solving the split equality problem in Hilbert spaces. It is, however, not easy to implement since its selection of the stepsize requires prior information on the norms of bounded linear operators. To avoid this difficulty, we propose several m...

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Bibliographic Details
Published in:Journal of inequalities and applications 2020-08, Vol.2020 (1), p.1-14, Article 214
Main Authors: Yu, Hai, Wang, Fenghui
Format: Article
Language:English
Subjects:
Algorithms
Alternating CQ algorithm
Analysis
Applications of Mathematics
Computational geometry
Convexity
Hilbert space
Iterative algorithms
Linear operators
Mathematics
Mathematics and Statistics
Norms
Split equality problem
Variable stepsize
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Summary:In this paper, we study the alternating CQ algorithm for solving the split equality problem in Hilbert spaces. It is, however, not easy to implement since its selection of the stepsize requires prior information on the norms of bounded linear operators. To avoid this difficulty, we propose several modified algorithms in which the selection of the stepsize is independent of the norms. In particular, we consider the case whenever the convex sets involved are level sets of given convex functions.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02480-z