Advertisement

Applied Mathematics and Optimization

, Volume 31, Issue 3, pp 245–255 | Cite as

Holder continuity of solutions to a parametric variational inequality

  • Nguyen Dong Yen
Article

Abstract

We prove a Hölder continuity property of the locally unique solution to a parametric variational inequality without assuming differentiability of the given data.

Key words

Parametric variational inequality Hölder continuity Metric projection 

AMS classification

49J40 49K40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alt, W. (1983), Lipschitzian perturbations of infinite optimization problems, in: Mathematical Programming with Data Perturbations, II, edited by A. V. Fiacco, Marcel Dekker, New York, pp. 7–21.Google Scholar
  2. 2.
    Attouch, H., and Wets, R. J.-B. (1992), Quantitative stability of variational systems, II. A framework for nonlinear conditioning, SIAM J. Optim., 3:359–381.Google Scholar
  3. 3.
    Aubin, J.-P. (1984), Lipschitz behavior of solutions to convex minimization problems, Math. Oper. Res., 9:87–111.Google Scholar
  4. 4.
    Clarke, F. H. (1983), Optimization and Nonsmooth Analysis, Wiley Interscience, New York.Google Scholar
  5. 5.
    Dafermos, S. (1988), Sensitivity analysis in variational inequalities, Math. Oper. Res., 13:421–434.Google Scholar
  6. 6.
    Fiacco, A. V. (1983), Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York.Google Scholar
  7. 7.
    Harker, P. T., and Pang, J.-S. (1990), Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms, and applications, Math. Programming, 48:161–220.Google Scholar
  8. 8.
    Kyparisis, J. (1990), Solution differentiability for variational inequalities, Math. Programming, 48:285–301.Google Scholar
  9. 9.
    Mangasafian, O. L., and Shiau, T.-H. (1987), Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems, SIAM J. Control Optim., 25:583–595.Google Scholar
  10. 10.
    Qui, Y., and Magnanti, T. L. (1989), Sensitivity analysis for variational inequalities defined on polyhedral sets, Math. Oper. Res., 14:410–432.Google Scholar
  11. 11.
    Robinson, S. M. (1991), An implicit-function theorem for a class of nonsmooth functions, Math. Oper. Res., 16:292–309.Google Scholar
  12. 12.
    Rockafellar, R. T. (1985), Lipschitzian properties of multifunctions, Nonlinear Anal. TMA, 9:867–885.Google Scholar
  13. 13.
    Shapiro, A. (1987), On differentiability of metric projections in Rn, 1: Boundary case, Proc. Amer. Math. Soc., 99:123–128.Google Scholar
  14. 14.
    Shapiro, A. (1988), Sensitivity analysis of nonlinear programs and differentiability properties of metric projections, SIAM J. Control Optim., 26:628–645.Google Scholar
  15. 15.
    Shapiro, A. (1992), Perturbation analysis of optimization problems in Banach spaces, Numer. Funct. Anal. Optim., 13:97–116.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1995

Authors and Affiliations

  • Nguyen Dong Yen
    • 1
    • 2
  1. 1.Institute of MathematicsBo Ho, 10000 HanoiVietnam
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

Personalised recommendations