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Quasimonotone Quasivariational Inequalities: Existence Results and Applications

Author

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  • D. Aussel

    (Université de Perpignan)

  • J. Cotrina

    (Universidad Nacional de Ingeniería)

Abstract

A quasivariational inequality is a variational inequality in which the constraint set depends on the variable. Based on fixed point techniques, we prove various existence results under weak assumptions on the set-valued operator defining the quasivariational inequality, namely quasimonotonicity and lower or upper sign-continuity. Applications to quasi-optimization and traffic network are also considered.

Suggested Citation

  • D. Aussel & J. Cotrina, 2013. "Quasimonotone Quasivariational Inequalities: Existence Results and Applications," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 637-652, September.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0270-3
    DOI: 10.1007/s10957-013-0270-3
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    References listed on IDEAS

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    1. Samir Adly & Maïtine Bergounioux & Mohamed Ait Mansour, 2010. "Optimal control of a quasi-variational obstacle problem," Journal of Global Optimization, Springer, vol. 47(3), pages 421-435, July.
    2. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    3. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
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    5. A. Daniilidis & N. Hadjisavvas, 1999. "Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 525-536, September.
    6. 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.
    7. D. Aussel & J. J. Ye, 2008. "Quasiconvex Minimization on a Locally Finite Union of Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 1-16, October.
    8. Anna Nagurney & David Parkes & Patrizia Daniele, 2007. "The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox," Computational Management Science, Springer, vol. 4(4), pages 355-375, October.
    9. B. T. Kien & N. C. Wong & J. C. Yao, 2007. "On the Solution Existence of Generalized Quasivariational Inequalities with Discontinuous Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 515-530, December.
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    Citations

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    Cited by:

    1. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.
    2. Mircea Balaj & Marco Castellani & Massimiliano Giuli, 2023. "New criteria for existence of solutions for equilibrium problems," Computational Management Science, Springer, vol. 20(1), pages 1-16, December.
    3. John Cotrina & Michel Théra & Javier Zúñiga, 2020. "An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 336-355, November.
    4. Maria Bernadette Donato & Monica Milasi & Antonio Villanacci, 2018. "Variational Formulation of a General Equilibrium Model with Incomplete Financial Markets and Numeraire Assets: Existence," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 425-451, November.
    5. Elisabetta Allevi & Didier Aussel & Rossana Riccardi & Domenico Scopelliti, 2024. "Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 344-370, January.
    6. 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.
    7. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.

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