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Multivalued Parametric Variational Inequalities with α-Pseudomonotone Maps

Author

Listed:
  • G. Kassay

    (Babes-Bolyai University)

  • J. Kolumban

    (Babes-Bolyai University)

Abstract

In this paper, we consider variational inequalities with pseudomonotone maps which depend on a parameter and study the behavior of their solutions. The main result gives sufficient conditions for the stability of the initial variational inequality problem under small perturbations of the parameter. As an application, we obtain a stability result for a class of parametric optimization problems.

Suggested Citation

  • G. Kassay & J. Kolumban, 2000. "Multivalued Parametric Variational Inequalities with α-Pseudomonotone Maps," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 35-50, October.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:1:d:10.1023_a:1004600631797
    DOI: 10.1023/A:1004600631797
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1976. "Regularity and Stability for Convex Multivalued Functions," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 130-143, May.
    2. Stella Dafermos, 1988. "Sensitivity Analysis in Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 421-434, August.
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    Cited by:

    1. P. Q. Khanh & L. M. Luu, 2007. "Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 329-339, June.
    2. Ren-you Zhong & Nan-jing Huang, 2010. "Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 454-472, December.

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