IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v23y2023i4d10.1007_s11067-023-09600-4.html
   My bibliography  Save this article

A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces

Author

Listed:
  • Pingjing Xia

    (Chongqing Normal University)

  • Gang Cai

    (Chongqing Normal University)

  • Qiao-Li Dong

    (Civil Aviation University of China)

Abstract

In this paper, we propose a new algorithm with inertial term and self-adaptive stepsize for solving the split variational inclusion problem (denoted by SVIP) in real Hilbert spaces. Under suitable conditions imposed on the parameters, we prove that our iterative scheme converges strongly to an element of the solution set of SVIP without the prior knowledge of the operator norm. Furthermore, we demonstrate that our suggested algorithm is efficient and achievable through some numerical experiments.

Suggested Citation

  • Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.
    • Handle: RePEc:kap:netspa:v:23:y:2023:i:4:d:10.1007_s11067-023-09600-4
    DOI: 10.1007/s11067-023-09600-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-023-09600-4
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-023-09600-4?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. Che, Haitao & Li, Meixia, 2016. "The conjugate gradient method for split variational inclusion and constrained convex minimization problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 426-438.
    2. 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.
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    4. 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.
    5. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    6. Q. L. Dong & Y. C. Tang & Y. J. Cho & Th. M. Rassias, 2018. "“Optimal” choice of the step length of the projection and contraction methods for solving the split feasibility problem," Journal of Global Optimization, Springer, vol. 71(2), pages 341-360, June.
    Full references (including those not matched with items on IDEAS)

    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. Pawicha Phairatchatniyom & Poom Kumam & Yeol Je Cho & Wachirapong Jirakitpuwapat & Kanokwan Sitthithakerngkiet, 2019. "The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications," Mathematics, MDPI, vol. 7(6), pages 1-22, June.
    2. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.
    3. Che, Haitao & Li, Meixia, 2016. "The conjugate gradient method for split variational inclusion and constrained convex minimization problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 426-438.
    4. 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.
    5. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    6. Adisak Hanjing & Suthep Suantai, 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    7. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "A Hybrid Forward–Backward Algorithm and Its Optimization Application," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
    8. Kumar, Ajay & Thakur, Balwant Singh & Postolache, Mihai, 2024. "Dynamic stepsize iteration process for solving split common fixed point problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 498-511.
    9. Abdellatif Moudafi, 2014. "Computing the resolvent of composite operators," Documents de Travail 2014-02, CEREGMIA, Université des Antilles et de la Guyane.
    10. Panadda Thongpaen & Rattanakorn Wattanataweekul, 2021. "A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    11. Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    12. Dang Van Hieu & Jean Jacques Strodiot & Le Dung Muu, 2020. "An Explicit Extragradient Algorithm for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 476-503, May.
    13. Suthep Suantai & Narin Petrot & Manatchanok Khonchaliew, 2021. "Inertial Extragradient Methods for Solving Split Equilibrium Problems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    14. Mohammad Akram & Mohammad Dilshad & Arvind Kumar Rajpoot & Feeroz Babu & Rais Ahmad & Jen-Chih Yao, 2022. "Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    15. Ali Abkar & Elahe Shahrosvand & Azizollah Azizi, 2017. "The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 5(1), pages 1-18, February.
    16. Ahmed Alamer & Mohammad Dilshad, 2024. "Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem," Mathematics, MDPI, vol. 12(5), pages 1-16, March.
    17. 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.
    18. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    19. Bunyawee Chaloemyotphong & Atid Kangtunyakarn, 2019. "Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space," Mathematics, MDPI, vol. 7(11), pages 1-26, November.
    20. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500056 is not listed on IDEAS
    21. Shih-sen Chang & Jen-Chih Yao & Ching-Feng Wen & Liang-cai Zhao, 2020. "On the Split Equality Fixed Point Problem of Quasi-Pseudo-Contractive Mappings Without A Priori Knowledge of Operator Norms with Applications," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 343-360, 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:kap:netspa:v:23:y:2023:i:4:d:10.1007_s11067-023-09600-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.