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Jing Zhao, Haixia Wang, Chenzheng Guo, Several accelerated iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

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DOI: 10.23952/jnva.8.2024.5.04

Volume 8, Issue 5, 1 October 2024, Pages 747-770

 

Abstract. In the paper, we introduce several accelerated iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators. Based on the primal-dual method, we construct several iterative algorithms in a way that combines inertial technology and self-adaptive stepsizes such that the implementation of the algorithms does not need any prior information about bounded linear operator norm. Under suitable assumptions, we obtain the weak convergence of the proposed algorithms in real Hilbert spaces. As applications, we obtain relative iterative algorithms to solve the multiple-set split feasibility problem. Finally, the performance of the proposed algorithms is illustrated by numerical experiments.

 

How to Cite this Article:
J. Zhao, H. Wang, C. Guo, Several accelerated iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators, J. Nonlinear Var. Anal. 8 (2024), 747-770.