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Stability of Quasimonotone Variational Inequality Under Sign-Continuity

Author

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  • D. Aussel

    (Université de Perpignan Via Domitia)

  • J. Cotrina

    (Universidad Nacional de Ingeniería)

Abstract

Whenever the data of a Stampacchia variational inequality, that is, the set-valued operator and/or the constraint map, are subject to perturbations, then the solution set becomes a solution map, and the study of the stability of this solution map concerns its regularity. An important literature exists on this topic, and classical assumptions, for monotone or quasimonotone set-valued operators, are some upper or lower semicontinuity. In this paper, we limit ourselves to perturbations on the constraint map, and it is proved that regularity results for the solution maps can be obtained under some very weak regularity hypothesis on the set-valued operator, namely the lower or upper sign-continuity.

Suggested Citation

  • D. Aussel & J. Cotrina, 2013. "Stability of Quasimonotone Variational Inequality Under Sign-Continuity," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 653-667, September.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0272-1
    DOI: 10.1007/s10957-013-0272-1
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    References listed on IDEAS

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    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. D. Aussel & J. Cotrina, 2011. "Semicontinuity of the solution map of quasivariational inequalities," Journal of Global Optimization, Springer, vol. 50(1), pages 93-105, May.
    3. C. S. Lalitha & Guneet Bhatia, 2011. "Stability of Parametric Quasivariational Inequality of the Minty Type," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 281-300, February.
    4. M. B. Lignola & J. Morgan, 1999. "Generalized Variational Inequalities with Pseudomonotone Operators Under Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 213-220, April.
    5. N. D. Yen, 1995. "Lipschitz Continuity of Solutions of Variational Inequalities with a Parametric Polyhedral Constraint," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 695-708, August.
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    Cited by:

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    2. Didier Aussel & Asrifa Sultana & Vellaichamy Vetrivel, 2016. "On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 818-837, September.

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