Alternated inertial algorithms for split feasibility problems

We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the i...

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Bibliographic Details
Published inNumerical algorithms Vol. 95; no. 2; pp. 773 - 812
Main Authors Tan, Bing, Qin, Xiaolong, Wang, Xianfu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2024
Subjects
Algebra
Algorithms
Computer Science
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Alternated inertial method
47J30
65K15
47J20
CQ method
Signal processing
Split feasibility problem
Image restoration
47J25
Projection and contraction method
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ISSN1017-1398
1572-9265
DOI10.1007/s11075-023-01589-8

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Summary:We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01589-8