IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v70y2018i2d10.1007_s10898-017-0564-3.html
   My bibliography  Save this article

New extragradient-like algorithms for strongly pseudomonotone variational inequalities

Author

Listed:
  • Dang Hieu

    (College of Air Force)

  • Duong Viet Thong

    (National Economics University)

Abstract

The paper considers two extragradient-like algorithms for solving variational inequality problems involving strongly pseudomonotone and Lipschitz continuous operators in Hilbert spaces. The projection method is used to design the algorithms which can be computed more easily than the regularized method. The construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the modulus of strong pseudomonotonicity and the Lipschitz constant of the cost operator. Instead of that, the algorithms use variable stepsize sequences which are diminishing and non-summable. The numerical behaviors of the proposed algorithms on a test problem are illustrated and compared with those of several previously known algorithms.

Suggested Citation

  • Dang Hieu & Duong Viet Thong, 2018. "New extragradient-like algorithms for strongly pseudomonotone variational inequalities," Journal of Global Optimization, Springer, vol. 70(2), pages 385-399, February.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0564-3
    DOI: 10.1007/s10898-017-0564-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0564-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-017-0564-3?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. Alfredo Iusem & Mostafa Nasri, 2011. "Korpelevich’s method for variational inequality problems in Banach spaces," Journal of Global Optimization, Springer, vol. 50(1), pages 59-76, May.
    2. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    3. Yu. Malitsky & V. Semenov, 2015. "A hybrid method without extrapolation step for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 61(1), pages 193-202, January.
    4. E. Allevi & A. Gnudi & I.V. Konnov, 2004. "Generalized Vector Variational Inequalities over Countable Product of Sets," Journal of Global Optimization, Springer, vol. 30(2), pages 155-167, November.
    5. Pham Khanh & Phan Vuong, 2014. "Modified projection method for strongly pseudomonotone variational inequalities," Journal of Global Optimization, Springer, vol. 58(2), pages 341-350, February.
    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. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2019. "Modified extragradient-like algorithms with new stepsizes for variational inequalities," Computational Optimization and Applications, Springer, vol. 73(3), pages 913-932, July.
    2. 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.
    3. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "Strong Convergent Theorems Governed by Pseudo-Monotone Mappings," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    4. Trinh Ngoc Hai, 2020. "Two modified extragradient algorithms for solving variational inequalities," Journal of Global Optimization, Springer, vol. 78(1), pages 91-106, September.
    5. Ming Lei & Yiran He, 2021. "An Extragradient Method for Solving Variational Inequalities without Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 432-446, February.
    6. 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.
    7. 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.

    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. Gang Cai & Qiao-Li Dong & Yu Peng, 2021. "Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 447-472, February.
    2. 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.
    3. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2019. "Modified extragradient-like algorithms with new stepsizes for variational inequalities," Computational Optimization and Applications, Springer, vol. 73(3), pages 913-932, July.
    4. 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.
    5. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    6. Dang Hieu & Pham Ky Anh & Le Dung Muu, 2017. "Modified hybrid projection methods for finding common solutions to variational inequality problems," Computational Optimization and Applications, Springer, vol. 66(1), pages 75-96, January.
    7. 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.
    8. 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.
    9. Lateef Olakunle Jolaoso & Christian Chibueze Okeke & Yekini Shehu, 2021. "Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces," Networks and Spatial Economics, Springer, vol. 21(4), pages 873-903, December.
    10. Yu. Malitsky & V. Semenov, 2015. "A hybrid method without extrapolation step for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 61(1), pages 193-202, January.
    11. Shin-ya Matsushita & Li Xu, 2014. "On Finite Convergence of Iterative Methods for Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 701-715, June.
    12. Xiaomei Dong & Xingju Cai & Deren Han & Zhili Ge, 2020. "Solving a Class of Variational Inequality Problems with a New Inexact Strategy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-20, January.
    13. Yanlai Song & Omar Bazighifan, 2022. "A New Alternative Regularization Method for Solving Generalized Equilibrium Problems," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    14. Yanlai Song & Omar Bazighifan, 2022. "Modified Inertial Subgradient Extragradient Method with Regularization for Variational Inequality and Null Point Problems," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    15. Dang Hieu, 2017. "New subgradient extragradient methods for common solutions to equilibrium problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 571-594, July.
    16. Chinedu Izuchukwu & Yekini Shehu, 2021. "New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems Beyond Monotonicity," Networks and Spatial Economics, Springer, vol. 21(2), pages 291-323, June.
    17. 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.
    18. Yekini Shehu & Olaniyi S. Iyiola & Duong Viet Thong & Nguyen Thi Cam Van, 2021. "An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 213-242, April.
    19. Trinh Ngoc Hai, 2020. "Two modified extragradient algorithms for solving variational inequalities," Journal of Global Optimization, Springer, vol. 78(1), pages 91-106, September.
    20. P. E. Maingé & M. L. Gobinddass, 2016. "Convergence of One-Step Projected Gradient Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 146-168, October.

    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:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0564-3. 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.