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Limit vector variational inequalities and market equilibrium problems

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Abstract

In a finite-dimensional setting we investigate the solvability of a general vector variational inequality via the convergence of solutions of suitable approximating vector variational inequalities defined with more regular data. The theoretical results obtained in a very general framework are successfully applied to the study of a vector market equilibrium problem where instead of exact values of the cost mapping, feasible set and order cone, only approximation sequences of these data are available.

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Acknowledgements

In this work, the second author was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, Project No. 1.13556.2019/13.1 and was also supported by Russian Foundation for Basic Research, Project No. 19-01-00431.

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Authors and Affiliations

  1. Dipartimento di Matematica per le Scienze Economiche, Finanziarie ed Attuariali, Università Cattolica del Sacro Cuore, Via Necchi 9, 20123, Milan, Italy

    M. Bianchi

  2. Department of System Analysis and Information Technologies, Kazan University, ul. Kremlevskaya 18, Kazan, Russia, 420008

    I. V. Konnov

  3. Dipartimento di Matematica e Applicazioni, Università degli Studi Milano-Bicocca, Via Cozzi 55, 20125, Milan, Italy

    R. Pini

Authors
  1. M. Bianchi
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  2. I. V. Konnov
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  3. R. Pini
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Correspondence to R. Pini.

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Bianchi, M., Konnov, I.V. & Pini, R. Limit vector variational inequalities and market equilibrium problems. Optim Lett 15, 817–832 (2021). https://doi.org/10.1007/s11590-019-01500-2

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  • DOI: https://doi.org/10.1007/s11590-019-01500-2

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