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

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...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2018-11, Vol.22 (5), p.1223-1239
Main Authors: Anh, L. Q., Hung, N. V.
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Cones
Econometrics
Equilibrium
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Well posed problems
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Summary: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.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-018-0569-2