A relaxed projection method using a new linesearch for the split feasibility problem

Suthep Suantai; Suparat Kesornprom; Nattawut Pholasa; Yeol Je Cho; Prasit Cholamjiak; Suthep Suantai; Suparat Kesornprom; Nattawut Pholasa; Yeol Je Cho; Prasit Cholamjiak

doi:10.3934/math.2021163

AIMS Mathematics

2021, Volume 6, Issue 3: 2690-2703. doi: 10.3934/math.2021163

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Research article

A relaxed projection method using a new linesearch for the split feasibility problem

1.
Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand
2.
School of Science, University of Phayao, Phayao 56000, Thailand
3.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P. R. China, and Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

Received: 23 November 2020 Accepted: 28 December 2020 Published: 04 January 2021
MSC : 47H10, 54H25

In this work, we propose a new relaxed projection algorithm for the split feasibility problem with a new linesearch. The proposed method does not require the computation on the matrix inverse and the largest eigenvalue of the matrix. We then prove some weak convergence theorems under suitable conditions in the framework of Hilbert spaces. Finally, we give some numerical examples in signal processing to validate the theoretical analysis results. The obtained results improve the corresponding results in the literature.
- split feasibility problem,
- $ CQ $-algorithm,
- Hilbert space,
- linesearch,
- signal recovery
Citation: Suthep Suantai, Suparat Kesornprom, Nattawut Pholasa, Yeol Je Cho, Prasit Cholamjiak. A relaxed projection method using a new linesearch for the split feasibility problem[J]. AIMS Mathematics, 2021, 6(3): 2690-2703. doi: 10.3934/math.2021163

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Abstract

In this work, we propose a new relaxed projection algorithm for the split feasibility problem with a new linesearch. The proposed method does not require the computation on the matrix inverse and the largest eigenvalue of the matrix. We then prove some weak convergence theorems under suitable conditions in the framework of Hilbert spaces. Finally, we give some numerical examples in signal processing to validate the theoretical analysis results. The obtained results improve the corresponding results in the literature.

References

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