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On ill-posedness and stability of tensor variational inequalities: application to an economic equilibrium

Author

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  • Annamaria Barbagallo

    (University of Naples Federico II)

  • Serena Guarino Lo Bianco

    (University of Naples Federico II)

Abstract

The general tensor variational inequalities, recently introduced in Barbagallo et al. (J Nonconvex Anal 19:711–729, 2018), are very useful in order to analyze economic equilibrium models. For this reason, the study of existence and regularity results for such inequalities has an important rule to the light of applications. To this aim, we start to consider some existence and uniqueness theorems for tensor variational inequalities. Then, we investigate on the approximation of solutions to tensor variational inequalities by using suitable perturbed tensor variational inequalities. We establish the convergence of solutions to the regularized tensor variational inequalities to a solution of the original tensor variational inequality making use of the set convergence in Kuratowski’s sense. After that, we focus our attention on some stability results. At last, we apply the theoretical results to examine a general oligopolistic market equilibrium problem.

Suggested Citation

  • Annamaria Barbagallo & Serena Guarino Lo Bianco, 2020. "On ill-posedness and stability of tensor variational inequalities: application to an economic equilibrium," Journal of Global Optimization, Springer, vol. 77(1), pages 125-141, May.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:1:d:10.1007_s10898-019-00788-9
    DOI: 10.1007/s10898-019-00788-9
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    References listed on IDEAS

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    1. Yong Wang & Zheng-Hai Huang & Liqun Qi, 2018. "Global Uniqueness and Solvability of Tensor Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 137-152, April.
    2. Xue-Li Bai & Zheng-Hai Huang & Yong Wang, 2016. "Global Uniqueness and Solvability for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 72-84, July.
    3. SALINETTI, Gabriella & WETS, Roger J.-B., 1979. "On the convergence of sequences of convex sets in finite dimensions," LIDAM Reprints CORE 352, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Dafermos, Stella & Nagurney, Anna, 1987. "Oligopolistic and competitive behavior of spatially separated markets," Regional Science and Urban Economics, Elsevier, vol. 17(2), pages 245-254.
    5. Yisheng Song & Liqun Qi, 2015. "Properties of Some Classes of Structured Tensors," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 854-873, June.
    6. Maolin Che & Liqun Qi & Yimin Wei, 2016. "Positive-Definite Tensors to Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 475-487, February.
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    Cited by:

    1. Francesca Anceschi & Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "Inverse Tensor Variational Inequalities and Applications," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 570-589, February.
    2. Wenjie Mu & Jianghua Fan, 2022. "Existence results for solutions of mixed tensor variational inequalities," Journal of Global Optimization, Springer, vol. 82(2), pages 389-412, February.
    3. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "A random time-dependent noncooperative equilibrium problem," Computational Optimization and Applications, Springer, vol. 84(1), pages 27-52, January.

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