IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v121y2004i1d10.1023_bjota.0000026271.19947.05.html
   My bibliography  Save this article

Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods

Author

Listed:
  • R. U. Verma

    (University of Toledo)

Abstract

Let K be a nonempty closed convex subset of a real Hilbert space H. The approximate solvability of a system of nonlinear variational inequality problems, based on the convergence of projection methods, is discussed as follows: find an element (x*, y*)∈K×K such that $$\begin{gathered} \left\langle {\rho {\rm T}(y^* ,x^* ) + x^* - y^* ,x - x^* } \right\rangle \geqslant 0,{\text{ }}\forall x \in K{\text{ and }}\rho > 0, \hfill \\ \left\langle {\eta {\rm T}(x^* ,y^* ) + y^* - x^* ,x - x^* } \right\rangle \geqslant 0,{\text{ }}\forall x \in K{\text{ and }}\eta > 0, \hfill \\ \end{gathered}$$ where T: K×K→H is a nonlinear mapping on K×K.

Suggested Citation

  • R. U. Verma, 2004. "Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 203-210, April.
    • Handle: RePEc:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026271.19947.05
    DOI: 10.1023/B:JOTA.0000026271.19947.05
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTA.0000026271.19947.05
    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/B:JOTA.0000026271.19947.05?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. N.H. Xiu & J.Z. Zhang, 2002. "Local Convergence Analysis of Projection-Type Algorithms: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 211-230, October.
    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. Wu, Zeng-bao & Zou, Yun-zhi & Huang, Nan-jing, 2016. "A class of global fractional-order projective dynamical systems involving set-valued perturbations," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 23-33.
    2. P. E. Maingé, 2008. "New Approach to Solving a System of Variational Inequalities and Hierarchical Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 459-477, September.
    3. Q. Z. Yang, 2006. "On a Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 547-549, September.
    4. R. P. Agarwal & R. U. Verma, 2010. "Inexact A-Proximal Point Algorithm and Applications to Nonlinear Variational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 431-444, March.
    5. R. U. Verma, 2006. "A-Monotonicity and Its Role in Nonlinear Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 457-467, June.
    6. R. U. Verma, 2006. "General System of A-Monotone Nonlinear Variational Inclusion Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 151-157, October.
    7. Changqun Wu & Meijuan Shang & Xiaolong Qin, 2007. "A General Projection Method for the System of Relaxed Cocoercive Variational Inequalities in Hilbert Spaces," Modern Applied Science, Canadian Center of Science and Education, vol. 1(3), pages 1-24, September.
    8. Kyung Soo Kim, 2018. "System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space," Mathematics, MDPI, vol. 6(10), pages 1-12, 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. 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.
    2. Changyu Wang & Qian Liu & Cheng Ma, 2013. "Smoothing SQP algorithm for semismooth equations with box constraints," Computational Optimization and Applications, Springer, vol. 55(2), pages 399-425, June.

    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:121:y:2004:i:1:d:10.1023_b:jota.0000026271.19947.05. 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.