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A new self-adaptive CQ algorithm with an application to the LASSO problem

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Abstract

In this paper, we introduce a new self-adaptive CQ algorithm for solving split feasibility problems in real Hilbert spaces. The algorithm is designed, such that the stepsizes are directly computed at each iteration. We also consider the corresponding relaxed CQ algorithm for the proposed method. Under certain mild conditions, we establish weak convergence of the proposed algorithm as well as strong convergence of its hybrid-type variant. Finally, numerical examples illustrating the efficiency of our algorithm in solving the LASSO problem are presented.

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Acknowledgements

The authors would like to thank the editor and the reviewers for their constructive suggestions and comments, which greatly improve the manuscript.

The second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No.101.01-2017.08. His research is also partially supported by the Vietnam Institute for Advanced Study in Mathematics and by UTC under Grant T2018-CB-002.

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Authors and Affiliations

  1. Faculty of Mathematics, Mechanics, and Informatics, Vietnam National University, Hanoi, Vietnam

    Pham Ky Anh & Vu Tien Dung

  2. Department of Mathematics, University of Transport and Communications, Hanoi, Vietnam

    Nguyen The Vinh

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  1. Pham Ky Anh
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  2. Nguyen The Vinh
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  3. Vu Tien Dung
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Correspondence to Nguyen The Vinh.

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Anh, P.K., Vinh, N.T. & Dung, V.T. A new self-adaptive CQ algorithm with an application to the LASSO problem. J. Fixed Point Theory Appl. 20, 142 (2018). https://doi.org/10.1007/s11784-018-0620-8

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  • DOI: https://doi.org/10.1007/s11784-018-0620-8

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