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Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints

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Abstract

In this paper we consider strong bilevel vector equilibrium problems and introduce the concepts of Levitin–Polyak well-posedness and Levitin–Polyak well-posedness in the generalized sense for such problems. The notions of upper/lower semicontinuity involving variable cones for vector-valued mappings and their properties are proposed and studied. Using these generalized semicontinuity notions, we investigate sufficient and/or necessary conditions of the Levitin–Polyak well-posedness for the reference problems. Some metric characterizations of these Levitin–Polyak well-posedness concepts in the behavior of approximate solution sets are also discussed. As an application, we consider the special case of traffic network problems with equilibrium constraints.

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Acknowledgements

The authors wish to thank the anonymous referees for the careful reviews and valuable comments that helped us significantly improve the presentation of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2017.18.

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Cantho University, Cantho, Vietnam

    L. Q. Anh

  2. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    N. V. Hung

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    N. V. Hung

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  1. L. Q. Anh
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  2. N. V. Hung
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Correspondence to N. V. Hung.

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Anh, L.Q., Hung, N.V. Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints. Positivity 22, 1223–1239 (2018). https://doi.org/10.1007/s11117-018-0569-2

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  • DOI: https://doi.org/10.1007/s11117-018-0569-2

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