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A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces

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  • M. Castellani

    (Università degli Studi dell’Aquila)

  • M. Giuli

    (Università degli Studi dell’Aquila)

Abstract

New existence results for quasiequilibrium problems on unbounded feasible sets in a finite-dimensional space and without any assumption of monotonicity are established. The key point behind these results is a weak coercivity condition for a generalized game which extends a recent one proposed in Konnov and Dyabilkin (J Glob Optim 49:575–587, 2011) for equilibrium problems and an older one given in Cubiotti (Comput Math Appl 30:11–22, 1995) for quasiequilibrium problems. Some examples are also given.

Suggested Citation

  • M. Castellani & M. Giuli, 2019. "A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces," Journal of Global Optimization, Springer, vol. 75(1), pages 163-176, September.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:1:d:10.1007_s10898-019-00811-z
    DOI: 10.1007/s10898-019-00811-z
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    References listed on IDEAS

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    1. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    2. Bliemer, Michiel C. J. & Bovy, Piet H. L., 2003. "Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 501-519, July.
    3. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
    5. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.
    6. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
    7. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    8. Wei Jing-Yuan & Yves Smeers, 1999. "Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices," Operations Research, INFORMS, vol. 47(1), pages 102-112, February.
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    Cited by:

    1. Marco Castellani & Massimiliano Giuli, 2021. "A Generalized Ky Fan Minimax Inequality on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 343-357, August.

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