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Stability of Quasimonotone Variational Inequality Under Sign-Continuity

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Abstract

Whenever the data of a Stampacchia variational inequality, that is, the set-valued operator and/or the constraint map, are subject to perturbations, then the solution set becomes a solution map, and the study of the stability of this solution map concerns its regularity. An important literature exists on this topic, and classical assumptions, for monotone or quasimonotone set-valued operators, are some upper or lower semicontinuity. In this paper, we limit ourselves to perturbations on the constraint map, and it is proved that regularity results for the solution maps can be obtained under some very weak regularity hypothesis on the set-valued operator, namely the lower or upper sign-continuity.

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Acknowledgements

We would like to thank the referees for their valuable remarks and suggestions which improved the quality of the paper.

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Authors and Affiliations

  1. Lab. PROMES UPR CNRS 8521, Université de Perpignan Via Domitia, Perpignan, France

    D. Aussel

  2. IMCA, Instituto de Matemática y Ciencias Afines, Universidad Nacional de Ingeniería, Calle Los Biólogos 245 Urb. San Cesar, La Molina, Lima 12, Peru

    J. Cotrina

Authors
  1. D. Aussel
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  2. J. Cotrina
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Correspondence to D. Aussel.

Additional information

Communicated by Igor Konnov.

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Aussel, D., Cotrina, J. Stability of Quasimonotone Variational Inequality Under Sign-Continuity. J Optim Theory Appl 158, 653–667 (2013). https://doi.org/10.1007/s10957-013-0272-1

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  • DOI: https://doi.org/10.1007/s10957-013-0272-1

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