An Adaptive and Expanded Framework For Multiple-Operator Split Common Fixed Point Problems

Fenghui Wang () and Hai Yu ()
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Fenghui Wang: Luoyang Normal University
Hai Yu: Luoyang Normal University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 8, 25 pages

Abstract: Abstract This paper addresses the multiple-operator split common fixed point problem, a fundamental challenge with wide applications in signal processing and medical imaging. We propose new block iterative algorithms, extending existing approaches to handle more demicontractive operators. Our key contributions are: firstly, introducing adaptive step-size mechanisms that remove the need to estimate the norm of linear operators; secondly, developing extrapolated Landweber operators to enhance convergence; and thirdly, formulating a double cyclic projection method to enhance flexibility and efficiency. We establish the weak convergence of these methods under intermittent activation of operator blocks through theoretical analysis. Numerical experiments demonstrate the algorithms’ effectiveness and efficiency in solving tough problems.

Keywords: Split feasibility problem; Demicontractive operator; Landweber operator; 47J25; 47J20; 49N45; 65J15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02765-7

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