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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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
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Abstract	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.
AbstractList	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. 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.
ArticleNumber	50
Author	Chen, Yasong Cao, Yu Peng, Yishuo Shi, Luoyi
Author_xml	– sequence: 1 givenname: Yu surname: Cao fullname: Cao, Yu organization: School of Mathematical Sciences, Tiangong University – sequence: 2 givenname: Yishuo surname: Peng fullname: Peng, Yishuo organization: School of Mathematical Sciences, Tiangong University – sequence: 3 givenname: Yasong surname: Chen fullname: Chen, Yasong organization: School of Mathematical Sciences, Tiangong University – sequence: 4 givenname: Luoyi surname: Shi fullname: Shi, Luoyi email: shiluoyi@tiangong.edu.cn organization: School of Mathematical Sciences, Tiangong University
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Cites_doi	10.4169/amer.math.monthly.119.02.087 10.1007/s12190-024-02008-4 10.1080/02331934.2022.2158036 10.1007/s12190-023-01875-7 10.1088/0031-9155/51/10/001 10.1007/s40314-024-02618-5 10.1007/s11075-018-0504-4 10.1088/0266-5611/26/10/105018 10.1088/0266-5611/28/8/085004 10.1007/s11075-023-01589-8 10.1016/j.na.2012.11.013 10.1007/978-1-4419-9467-7 10.1088/0266-5611/20/4/014 10.1080/02331934.2014.895897 10.1186/1029-242X-2014-478 10.1007/s10957-022-02113-z
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Keywords	Split equality problem Self-adaptive step size 65K15 Signal recovery problem 90C30 The multiple-sets split Equality problem The alternated inertial technique
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Snippet	In this paper, we propose four novel CQ-algorithms to solve the split equality problem (SEP) in Hilbert spaces. These algorithms incorporate advanced... In this paper, we propose four novel CQ-algorithms to solve the split equality problem (SEP) in Hilbert spaces. These algorithms incorporate advanced...
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SubjectTerms	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
Title	CQ-algorithms for the related problems of split equality problem in Hilbert spaces
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