Skip to main content

Advertisement

SpringerLink
Log in

On a Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods

  • Technical Note
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Verma introduced a system of nonlinear variational inequalities and proposed projection methods to solve it. This system reduces to a variational inequality problem under certain conditions. So, at least in form, it can be regarded as a extension of a variational inequality problem. In this note, we show that solving this system coincides exactly with solving a variational inequality problem. Therefore, we conclude that it suffices to study the corresponding variational inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • VERMA, R. U., Projection Methods, Algorithms, and a New System of Nonlinear Variational Inequalities, Computers and Mathematics with Applications, Vol. 41, pp. 1025–1031, 2001.

    Article  MathSciNet  Google Scholar 

  • VERMA, R. U., Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods, Journal of Optimization Theory and Applications, Vol. 121, pp. 203–210, 2004.

    Article  MathSciNet  Google Scholar 

  • VERMA, R. U., Projection Methods and a New System of Cocoercive Variational Inequality Problems, International Journal of Differential Equations and Applications, Vol. 6, pp. 359–367, 2002.

    MathSciNet  Google Scholar 

  • NIE, H., LIU, Z., KIM, K. H., and KANG, S. M., A System of Nonlinear Variational Inequalities Involving Strongly Monotone and Pseudocontractive Mappings, Advances in Nonlinear Inequalities, Vol. 6, pp. 91–99, 2003.

    MathSciNet  Google Scholar 

  • FACCHINEI, F., and PANG, J. S., Finite-Dimensional Variational Inequality and Complementarity Problems, Vols. 1 and 2, Springer Verlag, New York, NY, 2003.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and LPMC, Nankai University, Tian-jin, P.R. China

    Q. Z. Yang (Professor)

Authors
  1. Q. Z. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Natural Science Foundation of China, Grant 10571134.

Communicated by M. J. Balas

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Q.Z. On a Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods. J Optim Theory Appl 130, 547–549 (2006). https://doi.org/10.1007/s10957-006-9117-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-006-9117-5

Key Words

Search

Navigation