Stability of approximating solutions to parametric bilevel vector equilibrium problems and applications

In this paper, we establish sufficient conditions for the approximate solution mappings of parametric bilevel equilibrium problems with stability properties such as upper semicontinuity, lower semicontinuity, Hausdorff lower semicontinuity, continuity and Hausdorff continuity. Moreover, we also appl...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 38; no. 2; pp. 1 - 17
Main Authors Van Hung, Nguyen, Hai, Nguyen Minh
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Continuity
Equilibrium
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Stability
90C31
Bilevel vector equilibrium problem
49J53
Upper (lower) semicontinuity
49J40
Traffic network problems with equilibrium constraints
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ISSN2238-3603
1807-0302
DOI10.1007/s40314-019-0823-7

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Summary:In this paper, we establish sufficient conditions for the approximate solution mappings of parametric bilevel equilibrium problems with stability properties such as upper semicontinuity, lower semicontinuity, Hausdorff lower semicontinuity, continuity and Hausdorff continuity. Moreover, we also apply these results to parametric traffic network problems with equilibrium constraints. Many examples are provided to ensure the essentialness of the assumptions.
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ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-019-0823-7