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

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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.

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Acknowledgements

The authors cordially thank the referees for their valuable comments and suggestions, which lead to a clearer presentation of this work. The first author was partially supported by PRIN 2017 Nonlinear Differential Problems via Variational, Topological and Set-valued Methods (Grant 2017AYM8XW) and the second author by INdAM GNAMPA Project 2019 Tecniche variazionali in problemi di ottimizzazione.

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  1. Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, Via Cintia, 80126, Naples, Italy

    Annamaria Barbagallo & Serena Guarino Lo Bianco

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  1. Annamaria Barbagallo
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  2. Serena Guarino Lo Bianco
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Correspondence to Annamaria Barbagallo.

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Barbagallo, A., Guarino Lo Bianco, S. On ill-posedness and stability of tensor variational inequalities: application to an economic equilibrium. J Glob Optim 77, 125–141 (2020). https://doi.org/10.1007/s10898-019-00788-9

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