CQ-algorithms for the related problems of split equality problem in Hilbert spaces

In this paper, we propose four novel CQ-algorithms to solve the split equality problem (SEP) in Hilbert spaces. These algorithms incorporate advanced techniques such as adaptive step sizes, alternate inertia, and dual projections, ensuring weak convergence under mild conditions. Additionally, we ext...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 208; no. 1; p. 50
Main Authors: Cao, Yu, Peng, Yishuo, Chen, Yasong, Shi, Luoyi
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2026
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Engineering
Half spaces
Hilbert space
Inertia
Iterative methods
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Partial differential equations
Radiation
Signal processing
Signal reconstruction
Theory of Computation
Split equality problem
Self-adaptive step size
65K15
Signal recovery problem
90C30
The multiple-sets split Equality problem
The alternated inertial technique
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, we propose four novel CQ-algorithms to solve the split equality problem (SEP) in Hilbert spaces. These algorithms incorporate advanced techniques such as adaptive step sizes, alternate inertia, and dual projections, ensuring weak convergence under mild conditions. Additionally, we extend the algorithms to address the multiple-set split equality problem (MSSEP) by introducing four new iterative methods, which also exhibit weak convergence. To validate the efficiency and superiority of our algorithms, we conduct numerical experiments on signal recovery problems. The results demonstrate that our algorithms outperform existing methods in terms of computational speed and accuracy. Key advantages of our approach include: adaptive step sizes that eliminate the need for prior knowledge of operator norms, alternated inertia to accelerate convergence while maintaining Fejer monotonicity, projections onto the intersection of half-spaces, which simplify computations and enhance efficiency. Our work provides a robust framework for solving SEP and MSSEP, with significant potential for applications in optimization, signal processing, and beyond.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02872-5