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Jing Zhao, Haixia Wang, Ningning Zhao, Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

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DOI: 10.23952/jnva.7.2023.1.01

Volume 7, Issue 1, 1 February 2023, Pages 1-22

 

Abstract. In the paper, we introduce two accelerated cyclic iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert spaces. Inspired by the primal-dual algorithm, our proposed algorithms combine inertial technique with the self-adaptive stepsizes such that the implementation of the algorithms does not need any prior information about bounded linear operator norms. The weak and strong convergence of the proposed algorithms are established under suitable assumptions. As applications, we obtain several iterative algorithms to solve the multiple-set split feasibility problem. Finally, numerical results are included to demonstrate the efficiency of the proposed iterative algorithms.

 

How to Cite this Article:
J. Zhao, H. Wang, N. Zhao, Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators, J. Nonlinear Var. Anal. 7 (2023), 1-22.