Skip to main content
Log in

Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities

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

Abstract

In this paper, we use the Wiener–Hopf equations technique to suggest and analyze new iterative methods for solving general quasimonotone variational inequalities. These new methods differ from previous known methods for solving variational inequalities.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Noor, M. A., General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119–121. 1988.

    Google Scholar 

  2. Noor, M. A., Wiener-Hopf Equations and Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 79, pp. 197–206, 1993.

    Google Scholar 

  3. Noor, M. A., Some Recent Advances in Variational Inequalities, Part 1: Basic Concepts, New Zealand Journal of Mathematics, Vol. 26, pp. 53–80, 1997.

    Google Scholar 

  4. Noor, M. A., Some Recent Advances in Variational Inequalities, Part 2: Other Concepts, New Zealand Journal of Mathematics, Vol. 26, pp. 229–255, 1997.

    Google Scholar 

  5. Noor, M. A., Some Iterative Techniques for General Monotone Variational Inequalities, Optimization, 1999.

  6. Noor, M. A., A Modified Extragradient Method for General Monotone Variational Inequalities, Computer Mathematics with Applications, Vol. 38, pp. 19–24, 1999.

    Google Scholar 

  7. Noor, M. A., Noor, K. I., and Rassias, T. M., Some Aspects of Variational Inequalities, Journal of Computational and Applied Mathematics, Vol. 47, pp. 285–312, 1993.

    Google Scholar 

  8. He, B., A Class of Projection and Contraction Methods for Monotone Variational Inequalities, Applied Mathematics and Optimization, Vol. 35, pp. 69–76, 1997.

    Google Scholar 

  9. Solodov, M. V., and Tseng, P., Modified Projection-Type Methods for Monotone Variational Inequalities, SIAM Journal on Control and Optimization, Vol. 34, pp. 1814–1836, 1996.

    Google Scholar 

  10. Tseng, P., A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings, SIAM Journal of Control and Optimization, 1999.

  11. Stampacchia, G., Formes Bilinearires Coercitives sur les Ensembles Convexes, Comptes Rendus de l'Academie des Sciences, Paris, Vol. 258, pp. 4413–4416, 1964.

    Google Scholar 

  12. Baiocchi, C., and Capelo, A., Variational and Quasi-Variational Inequalities, John Wiley and Sons, New York, New York, 1984.

    Google Scholar 

  13. Cottle, R. W., Giannessi, F., and Lions, J. L., Variational Inequalities and Complementarity Problems: Theory and Applications, John Wiley and Sons, New York, New York, 1980.

    Google Scholar 

  14. Giannessi, F., and Maugeri, A., Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, New York, 1995.

    Google Scholar 

  15. Glowinski, R., Lions, J. L., and TremoliÈres, R., Numerical Analysis of Variational Inequalities, North Holland, Amsterdam, Holland, 1981.

    Google Scholar 

  16. Glowinski, R., Numerical Methods for Nonlinear Variational Problems, North Holland, Amsterdam, Holland, 1984.

    Google Scholar 

  17. Noor, M. A., Some Algorithms for General Monotone Mixed Variational Inequalities, Mathematical and Computer Modelling, Vol. 29, pp. 1–9, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Noor, M.A., Al-Said, E.A. Wiener–Hopf Equations Technique for Quasimonotone Variational Inequalities. Journal of Optimization Theory and Applications 103, 705–714 (1999). https://doi.org/10.1023/A:1021796326831

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021796326831

Navigation