Skip to main content
SpringerLink
Log in

On the Stability of Generalized Vector Quasivariational Inequality Problems

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

Abstract

In this paper, we obtain some stability results for generalized vector quasivariational inequality problems. We prove that the solution set is a closed set and establish the upper semicontinuity property of the solution set for perturbed generalized vector quasivariational inequality problems. These results extend those obtained in Ref. 1. We obtain also the lower semicontinuity property of the solution set for perturbed classical variational inequalities. Several examples are given for the illustration of our results.

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

  1. GONG, L., Global Stability Result for the Generalized Quasivariational Inequality Problem, Journal of Optimization Theory and Applications, Vol. 70, pp. 365-375, 1991.

    Google Scholar 

  2. DAFERMOS, S., Sensitivity Analysis in Variational Inequalities, Mathematics of Operations Research, Vol. 13, pp. 421-434, 1988.

    Google Scholar 

  3. HARKER, P. T., and PANG, J. S., Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990.

    Google Scholar 

  4. TOBIN, R. L., Sensitivity Analysis for Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 48, pp. 191-204, 1986.

    Google Scholar 

  5. SIDDIQI, A. H., ANSARI, Q. H., and KHALIQ, A., On Vector Variational-Like Inequalities, Journal Mathematical Analysis and Applications, Vol. 84, pp. 171-180, 1995.

    Google Scholar 

  6. CHEN, G. Y., Existence of Solutions for a Vector Variational Inequality: An Extension of the Hartmann-Stampacchia Theorem, Journal of Optimization Theory and Applications, Vol. 74, pp. 445-456, 1992.

    Google Scholar 

  7. CHEN, G. Y., and LI, S. J., Existence of Solutions for a Generalized Vector Quasivariational Inequality, Journal of Optimization Theory and Applications, Vol. 90, pp. 321-334, 1996.

    Google Scholar 

  8. DANIILIDIS, A., and HADJISAVVS, N., Existence Theorems for Vector Variational Inequalities, Bulletin of the Australian Mathematical Society, Vol. 54, pp. 473-481, 1996.

    Google Scholar 

  9. GIANNESSI, F., Theorems of the Alternative, Quadratic Programs, and Complementary Problems, Variational Inequality and Complementary Problems, Edited by R. W. Cottle, F. Giannessi, and J. C. Lions, John Wiley and Sons, New York, NY, 1980.

    Google Scholar 

  10. KONNOV, V., and YAO, J. C., On the Generalized Vector Variational Inequality Problem, Journal of Mathematical Analysis and Applications, Vol. 206, pp. 42-58, 1997.

    Google Scholar 

  11. LEE, G. M., KIM, D. S., and LEE, B. S., On Generalized Vector Variational Inequality, Applied Mathematics Letters, Vol. 9, pp. 39-42, 1996.

    Google Scholar 

  12. DANIELE, P., and MAUGERI, A., Vector Variational Inequality and Modeling of a Continuum Traffic Equilibrium Problem, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Edited by F. Giannessi, Kluwer Academic Publishers, Doedrecht, Holland, Vol. 38, pp. 97-112, 2000.

    Google Scholar 

  13. YANG, X. Q., and GOH, C. J., Vector Variational Inequalities: Application to Vector Equilibria, Journal of Optimization Theory and Applications, Vol. 95, pp. 431-443, 1997.

    Google Scholar 

  14. YU, S. J., and YAO, J. C., On Vector Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 89, pp. 749-769, 1996.

    Google Scholar 

  15. AUBIN, J. P., and EKELAND, I., Applied Nonlinear Analysis, John Wiley and Sons, New York, NY, 1984.

    Google Scholar 

  16. KARAMARDIAN, S., and SCHAIBLE, S., Seven Kinds of Monotone Maps, Journal of Optimization Theory and Applications, Vol. 66, pp. 37-46, 1990.

    Google Scholar 

  17. TANINO, T., and SAWARAGI, Y., Stability of Nondominated Solutions in Multicriteria Decision Making, Journal of Optimization Theory and Applications, Vol. 30, pp. 229-253, 1980.

    Google Scholar 

Download references

Author information

Author notes

  1. S.J. Li (Associate Professor)

    Present address: Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong

Authors and Affiliations

  1. Department of Applied Mathematics, College of Sciences, Chongqing University, Chongqing, China

    S.J. Li (Associate Professor)

  2. Chinese Academy of Sciences, Institute of Systems Science, Beijing, China

    G.Y. Chen (Professor)

  3. Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong

    K.L. Teo (Chair Professor)

Authors
  1. S.J. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G.Y. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K.L. Teo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, S., Chen, G. & Teo, K. On the Stability of Generalized Vector Quasivariational Inequality Problems. Journal of Optimization Theory and Applications 113, 283–295 (2002). https://doi.org/10.1023/A:1014830925232

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014830925232

Search

Navigation