IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v94y1997i3d10.1023_a1022605117998.html
   My bibliography  Save this article

A Class of Combined Iterative Methods for Solving Variational Inequalities

Author

Listed:
  • I. V. Konnov

    (Kazan University)

Abstract

A general approach to constructing iterative methods that solve variational inequalities is proposed. It is based on combining, modifying, and extending ideas contained in various Newton-like methods. Various algorithms can be obtained with this approach. Their convergence is proved under weak assumptions. In particular, the main mapping need not be monotone. Some rates of convergence are also given.

Suggested Citation

  • I. V. Konnov, 1997. "A Class of Combined Iterative Methods for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 677-693, September.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:3:d:10.1023_a:1022605117998
    DOI: 10.1023/A:1022605117998
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022605117998
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022605117998?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. I. V. Konnov & S. Schaible & J. C. Yao, 2005. "Combined Relaxation Method for Mixed Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 309-322, August.
    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. Jiapeng Yan & Huifang Kong & Zhihong Man, 2022. "Recurrent Neural Network-Based Nonlinear Optimization for Braking Control of Electric Vehicles," Energies, MDPI, vol. 15(24), pages 1-17, December.
    2. R. Díaz Millán & O. P. Ferreira & J. Ugon, 2024. "Extragradient method with feasible inexact projection to variational inequality problem," Computational Optimization and Applications, Springer, vol. 89(2), pages 459-484, November.
    3. Y. J. Wang & N. H. Xiu & C. Y. Wang, 2001. "Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 641-656, December.
    4. Y. J. Wang & N. H. Xiu & J. Z. Zhang, 2003. "Modified Extragradient Method for Variational Inequalities and Verification of Solution Existence," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 167-183, October.

    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. Yonghong Yao & Yeong-Cheng Liou & Ngai-Ching Wong, 2013. "Superimposed optimization methods for the mixed equilibrium problem and variational inclusion," Journal of Global Optimization, Springer, vol. 57(3), pages 935-950, November.
    2. Uthai Kamraksa & Rabian Wangkeeree, 2011. "Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces," Journal of Global Optimization, Springer, vol. 51(4), pages 689-714, December.
    3. I. V. Konnov, 2001. "Combined Relaxation Method for Monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 327-340, November.
    4. I. V. Konnov, 2014. "Right-Hand Side Decomposition for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 221-238, January.
    5. Felipe Alvarez & Miguel Carrasco & Karine Pichard, 2005. "Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 966-984, November.
    6. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    7. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    8. L. C. Zeng & J. C. Yao, 2006. "Modified Combined Relaxation Method for General Monotone Equilibrium Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 469-483, December.
    9. E. Allevi & A. Gnudi & I. V. Konnov & G. Oggioni, 2018. "Evaluating the effects of environmental regulations on a closed-loop supply chain network: a variational inequality approach," Annals of Operations Research, Springer, vol. 261(1), pages 1-43, February.
    10. 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.
    11. I. V. Konnov, 1998. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 165-181, October.
    12. M. Castellani & M. Giuli, 2010. "On Equivalent Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 157-168, October.
    13. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    14. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.

    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:joptap:v:94:y:1997:i:3:d:10.1023_a:1022605117998. 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.