IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics0960077922000698.html
   My bibliography  Save this article

Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery

Author

Listed:
  • Cholamjiak, Watcharaporn
  • Dutta, Hemen

Abstract

In this paper, we introduce a new parallel algorithm by combining viscosity modification with parallel inertial two steps forward-backward splitting methods for approximating a solution of common inclusion problems. The strongly convergent theorems are established under some suitable conditions in Hilbert spaces. The applicability and advantages of the new parallel algorithm are presented by using to solve signal recovering problem in compressed sensing. The efficiency of the algorithm is shown by comparing it with some previous parallel algorithms.

Suggested Citation

  • Cholamjiak, Watcharaporn & Dutta, Hemen, 2022. "Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000698
    DOI: 10.1016/j.chaos.2022.111858
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922000698
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111858?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Heinz H. Bauschke & Patrick L. Combettes, 2001. "A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 248-264, May.
    2. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    3. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Suthep Suantai & Kunrada Kankam & Damrongsak Yambangwai & Watcharaporn Cholamjiak, 2022. "A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    2. Watchareepan Atiponrat & Pariwate Varnakovida & Pharunyou Chanthorn & Teeranush Suebcharoen & Phakdi Charoensawan, 2023. "Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations," Mathematics, MDPI, vol. 11(15), pages 1-20, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chanjuan Pan & Yuanheng Wang, 2019. "Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    2. Adamu, A. & Kitkuan, D. & Padcharoen, A. & Chidume, C.E. & Kumam, P., 2022. "Inertial viscosity-type iterative method for solving inclusion problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 445-459.
    3. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2021. "Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    4. Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    5. Lu-Chuan Ceng & Meijuan Shang, 2019. "Generalized Mann Viscosity Implicit Rules for Solving Systems of Variational Inequalities with Constraints of Variational Inclusions and Fixed Point Problems," Mathematics, MDPI, vol. 7(10), pages 1-18, October.
    6. Dang Hieu & Pham Ky Anh & Nguyen Hai Ha, 2021. "Regularization Proximal Method for Monotone Variational Inclusions," Networks and Spatial Economics, Springer, vol. 21(4), pages 905-932, December.
    7. Suthep Suantai & Kunrada Kankam & Damrongsak Yambangwai & Watcharaporn Cholamjiak, 2022. "A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    8. Peichao Duan & Xubang Zheng & Jing Zhao, 2018. "Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    9. Yanlai Song & Omar Bazighifan, 2022. "Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    10. Yanlai Song & Omar Bazighifan, 2022. "Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed Equilibrium Problem," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    11. Prasit Cholamjiak & Suparat Kesornprom & Nattawut Pholasa, 2019. "Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    12. Jenwit Puangpee & Suthep Suantai, 2020. "A New Accelerated Viscosity Iterative Method for an Infinite Family of Nonexpansive Mappings with Applications to Image Restoration Problems," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    13. Yanlai Song & Mihai Postolache, 2021. "Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    14. Kamonrat Sombut & Kanokwan Sitthithakerngkiet & Areerat Arunchai & Thidaporn Seangwattana, 2023. "An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    15. Suthep Suantai & Nontawat Eiamniran & Nattawut Pholasa & Prasit Cholamjiak, 2019. "Three-Step Projective Methods for Solving the Split Feasibility Problems," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    16. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    17. Shamshad Husain & Mohammed Ahmed Osman Tom & Mubashshir U. Khairoowala & Mohd Furkan & Faizan Ahmad Khan, 2022. "Inertial Tseng Method for Solving the Variational Inequality Problem and Monotone Inclusion Problem in Real Hilbert Space," Mathematics, MDPI, vol. 10(17), pages 1-16, September.
    18. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2024. "Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems," Networks and Spatial Economics, Springer, vol. 24(2), pages 425-459, June.
    19. Renli Liang & Yanqin Bai & Hai Xiang Lin, 2019. "An inexact splitting method for the subspace segmentation from incomplete and noisy observations," Journal of Global Optimization, Springer, vol. 73(2), pages 411-429, February.
    20. Li Wei & Yingzi Shang & Ravi P. Agarwal, 2019. "New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications," Mathematics, MDPI, vol. 7(5), pages 1-19, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000698. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.