IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v23y2023i1d10.1007_s11067-022-09569-6.html
   My bibliography  Save this article

A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities

Author

Listed:
  • Duong Viet Thong

    (Thu Dau Mot University)

  • Pham Ky Anh

    (Vietnam National University)

  • Vu Tien Dung

    (Vietnam National University)

  • Do Thi My Linh

    (Hanoi University of Industry)

Abstract

In this paper, we introduce a novel iterative method for finding the minimum-norm solution to a pseudomonotone variational inequality problem in Hilbert spaces. We establish strong convergence of the proposed method and its linear convergence under some suitable assumptions. Some numerical experiments are given to illustrate the performance of our method. Our result improves and extends some existing results in the literature.

Suggested Citation

  • Duong Viet Thong & Pham Ky Anh & Vu Tien Dung & Do Thi My Linh, 2023. "A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 23(1), pages 39-64, March.
    • Handle: RePEc:kap:netspa:v:23:y:2023:i:1:d:10.1007_s11067-022-09569-6
    DOI: 10.1007/s11067-022-09569-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-022-09569-6
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-022-09569-6?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. Rapeepan Kraikaew & Satit Saejung, 2014. "Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 399-412, November.
    2. Hongwei Liu & Jun Yang, 2020. "Weak convergence of iterative methods for solving quasimonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 491-508, November.
    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. Austine Efut Ofem & Jacob Ashiwere Abuchu & Hossam A. Nabwey & Godwin Chidi Ugwunnadi & Ojen Kumar Narain, 2023. "On Bilevel Monotone Inclusion and Variational Inequality Problems," Mathematics, MDPI, vol. 11(22), pages 1-28, November.

    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. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    2. Chinedu Izuchukwu & Yekini Shehu & Jen-Chih Yao, 2022. "New inertial forward-backward type for variational inequalities with Quasi-monotonicity," Journal of Global Optimization, Springer, vol. 84(2), pages 441-464, October.
    3. Duong Viet Thong & Xiao-Huan Li & Vu Tien Dung & Pham Thi Huong Huyen & Hoang Thi Thanh Tam, 2024. "Using Double Inertial Steps Into the Single Projection Method with Non-monotonic Step Sizes for Solving Pseudomontone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 24(1), pages 1-26, March.
    4. Jamilu Abubakar & Poom Kumam & Habib ur Rehman & Abdulkarim Hassan Ibrahim, 2020. "Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator," Mathematics, MDPI, vol. 8(4), pages 1-25, April.
    5. 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.
    6. Pham Ngoc Anh, 2024. "Relaxed projection methods for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 90(4), pages 909-930, December.
    7. Zhong-bao Wang & Xue Chen & Jiang Yi & Zhang-you Chen, 2022. "Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities," Journal of Global Optimization, Springer, vol. 82(3), pages 499-522, March.
    8. Gang Cai & Aviv Gibali & Olaniyi S. Iyiola & Yekini Shehu, 2018. "A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 219-239, July.
    9. Xin He & Nan-jing Huang & Xue-song Li, 2022. "Modified Projection Methods for Solving Multi-valued Variational Inequality without Monotonicity," Networks and Spatial Economics, Springer, vol. 22(2), pages 361-377, June.
    10. Lu-Chuan Ceng & Yekini Shehu & Jen-Chih Yao, 2022. "Modified Mann Subgradient-like Extragradient Rules for Variational Inequalities and Common Fixed Points Involving Asymptotically Nonexpansive Mappings," Mathematics, MDPI, vol. 10(5), pages 1-20, February.
    11. Lu-Chuan Ceng & Adrian Petruşel & Jen-Chih Yao, 2019. "On Mann Viscosity Subgradient Extragradient Algorithms for Fixed Point Problems of Finitely Many Strict Pseudocontractions and Variational Inequalities," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    12. Yun-Ling Cui & Lu-Chuan Ceng & Fang-Fei Zhang & Cong-Shan Wang & Jian-Ye Li & Hui-Ying Hu & Long He, 2022. "Modified Mann-Type Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points Implicating Countably Many Nonexpansive Operators," Mathematics, MDPI, vol. 10(11), pages 1-26, June.
    13. Bing Tan & Xiaolong Qin & Jen-Chih Yao, 2022. "Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems," Journal of Global Optimization, Springer, vol. 82(3), pages 523-557, March.
    14. Tingting Cai & Dongmin Yu & Huanan Liu & Fengkai Gao, 2022. "RETRACTED: Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach," Mathematics, MDPI, vol. 10(13), pages 1-14, July.
    15. Lateef Olakunle Jolaoso & Adeolu Taiwo & Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2020. "A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 744-766, June.
    16. Duong Viet Thong & Phan Tu Vuong & Pham Ky Anh & Le Dung Muu, 2022. "A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 22(4), pages 803-829, December.
    17. Lu-Chuan Ceng & Xiaolong Qin & Yekini Shehu & Jen-Chih Yao, 2019. "Mildly Inertial Subgradient Extragradient Method for Variational Inequalities Involving an Asymptotically Nonexpansive and Finitely Many Nonexpansive Mappings," Mathematics, MDPI, vol. 7(10), pages 1-19, September.
    18. Lu-Chuan Ceng & Adrian Petruşel & Ching-Feng Wen & Jen-Chih Yao, 2019. "Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings," Mathematics, MDPI, vol. 7(9), pages 1-19, September.
    19. Cholamjiak, Watcharaporn & Suparatulatorn, Raweerote, 2023. "Strong convergence of a modified extragradient algorithm to solve pseudomonotone equilibrium and application to classification of diabetes mellitus," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    20. Lu-Chuan Ceng & Ching-Feng Wen & Yeong-Cheng Liou & Jen-Chih Yao, 2022. "On Strengthened Inertial-Type Subgradient Extragradient Rule with Adaptive Step Sizes for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive Mappings," Mathematics, MDPI, vol. 10(6), pages 1-21, March.

    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:1:d:10.1007_s11067-022-09569-6. 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.