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Positivity

, Volume 22, Issue 1, pp 159–190 | Cite as

Second-order sequence-based necessary optimality conditions in constrained nonsmooth vector optimization and applications

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Abstract

Several notions of sequential directional derivatives and sequential local approximations are introduced. Under (first-order) Hadamard differentiability assumptions of the data at the point of study, these concepts are utilized to analyze second-order necessary optimality conditions, which rely on given sequences, for local weak solutions in nonsmooth vector optimization problems with constraints. Some applications to minimax programming problems are also derived.

Keywords

Nonsmooth vector optimization Sequence-based necessary optimality condition Weak solution Second-order sequential tangent set Second-order sequential directional derivative 

Mathematics Subject Classification

90C29 90C46 49K27 26B05 

Notes

Acknowledgements

The author would like to thank the editor and an anonymous referee for their valuable remarks and suggestions, which have helped him to improve the paper.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Economics-Hochiminh CityHochiminh CityVietnam

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