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Journal of Optimization Theory and Applications

, Volume 171, Issue 2, pp 643–665 | Cite as

Optimality Condition for Local Efficient Solutions of Vector Equilibrium Problems via Convexificators and Applications

  • Do Van  Luu
Article

Abstract

Fritz John and Karush–Kuhn–Tucker necessary conditions for local efficient solutions of constrained vector equilibrium problems in Banach spaces in which those solutions are regular in the sense of Ioffe via convexificators are established. Under suitable assumptions on generalized convexity, sufficient conditions are derived. Some applications to constrained vector variational inequalities and constrained vector optimization problems are also given.

Keywords

Vector equilibrium problems Vector variational inequalities  Vector optimization problems Regular points in the sense of Ioffe  Fritz John and Karush–Kuhn–Tucker optimality conditions Convexificators 

Mathematics Subject Classification

90C46 91B50 49J52 

Notes

Acknowledgments

The author is grateful to the referees for their valuable comments and suggestions which improve the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2014.61.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of Mathematics, Vietnam Academy of Science and TechnologyThang Long UniversityHanoiVietnam

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