Journal of Global Optimization

, Volume 70, Issue 2, pp 437–453 | Cite as

Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems



This paper presents primal and dual second-order Fritz John necessary conditions for weak efficiency of nonsmooth vector equilibrium problems involving inequality, equality and set constraints in terms of the Páles–Zeidan second-order directional derivatives. Dual second-order Karush–Kuhn–Tucker necessary conditions for weak efficiency are established under suitable second-order constraint qualifications.


Primal and dual second-order necessary efficiency conditions Páles–Zeidan second-order directional derivatives First and second-order tangent vectors Second-order constraint qualifications 

Mathematics Subject Classification

90C46 90C29 



The author is grateful to the referees for their valuable comments and suggestions which improve the paper. This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.301


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

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

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