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Mathematical Methods of Operations Research

, Volume 79, Issue 2, pp 163–177 | Cite as

Efficient solutions and optimality conditions for vector equilibrium problems

  • Do Van LuuEmail author
  • Dinh Dieu Hang
Original Article

Abstract

Necessary optimality conditions for efficient solutions of unconstrained and vector equilibrium problems with equality and inequality constraints are derived. Under assumptions on generalized convexity, necessary optimality conditions for efficient solutions become sufficient optimality conditions. Note that it is not required here that the ordering cone in the objective space has a nonempty interior.

Keywords

Efficient solutions Quasirelative interiors Quasiinteriors  Clarke subdifferentials Dini subdifferentials \(\partial \)-Pseudoconvex functions \(\partial _D\)-Quasiconvex functions 

Mathematics Subject Classification (2000)

90C46 91B50 49J52 

Notes

Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.Department of Basic SciencesThai Nguyen University of Information and Communication TechnologyThai NguyenVietnam

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