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Journal of Optimization Theory and Applications

, Volume 160, Issue 2, pp 510–526 | Cite as

Necessary and Sufficient Conditions for Efficiency Via Convexificators

  • Do Van Luu
Article

Abstract

Based on the extended Ljusternik Theorem by Jiménez-Novo, necessary conditions for weak Pareto minimum of multiobjective programming problems involving inequality, equality and set constraints in terms of convexificators are established. Under assumptions on generalized convexity, necessary conditions for weak Pareto minimum become sufficient conditions.

Keywords

Fritz John and Karush–Kuhn–Tucker necessary and sufficient conditions for weak Pareto minimum Upper and lower convexificators Upper regular convexificators Quasiconvex functions Scalarly K-asymptotic pseudoconvex functions 

Notes

Acknowledgements

The author thanks the referees for their valuable comments and suggestions. This research was supported by National Foundation for Science and Technology Development of Vietnam.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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