Levitin-Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints. (English) Zbl 1402.49022
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.
MSC:
| 49K40 | Sensitivity, stability, well-posedness |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 90C29 | Multi-objective and goal programming |
| 90C31 | Sensitivity, stability, parametric optimization |
| 90B20 | Traffic problems in operations research |
Keywords:
bilevel equilibrium problems; traffic network problems with equilibrium constraints; Levitin-Polyak well-posedness; upper (lower) semicontinuity involving variable coneReferences:
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