Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints

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Abstract

In this paper, we consider a class of multiobjective problems with equilibrium constraints. Our first task is to extend the existing constraint qualifications for mathematical problems with equilibrium constraints from the single-objective case to the multiobjective case, and our second task is to derive some stationarity conditions under the proper Pareto sense for the considered problem. After doing that, we devote ourselves to investigating the relationships among the extended constraint qualifications and the proper Pareto stationarity conditions.

Keywords

Multiobjective problem with equilibrium constraints Constraint qualification Proper Pareto stationarity condition 

Mathematics Subject Classification

90C29 90C33 90C46 

Notes

Acknowledgements

This work was supported in part by NSFC (Nos. 11671250, 11431004, 11601458), HKBU Grants (Nos. FRG1/16-17/007, FRG2/16-17/101, RC-NACAN-ZHANG J), and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Peng Zhang
    • 1
  • Jin Zhang
    • 2
  • Gui-Hua Lin
    • 1
  • Xinmin Yang
    • 3
  1. 1.School of ManagementShanghai UniversityShanghaiChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityHong KongChina
  3. 3.College of Mathematics ScienceChongqing Normal UniversityChongqingChina

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