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Quasimonotone Quasivariational Inequalities: Existence Results and Applications

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Abstract

A quasivariational inequality is a variational inequality in which the constraint set depends on the variable. Based on fixed point techniques, we prove various existence results under weak assumptions on the set-valued operator defining the quasivariational inequality, namely quasimonotonicity and lower or upper sign-continuity. Applications to quasi-optimization and traffic network are also considered.

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Acknowledgement

The authors would like to thank Nicolas Hadjisavvas for providing elements leading to statement of Proposition 4.3. Thanks are also addressed to the referees for their valuable comments which helped improve the quality of the paper.

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Authors and Affiliations

  1. Lab. PROMES, UPR CNRS 8521, Université de Perpignan, 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.

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Communicated by Igor Konnov.

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Aussel, D., Cotrina, J. Quasimonotone Quasivariational Inequalities: Existence Results and Applications. J Optim Theory Appl 158, 637–652 (2013). https://doi.org/10.1007/s10957-013-0270-3

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  • DOI: https://doi.org/10.1007/s10957-013-0270-3

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