Applied Mathematics & Optimization

, Volume 77, Issue 3, pp 515–539 | Cite as

On Necessary Optimality Conditions for Nonsmooth Vector Optimization Problems with Mixed Constraints in Infinite Dimensions

Article

Abstract

In this note, we develop first- and second-order necessary optimality conditions for local weak solutions in nonsmooth vector optimization problems subject to mixed constraints in infinite-dimensional settings. To this aim, we use some set-valued directional derivatives of the Hadamard type and tangent sets, and impose (first-order) Hadamard differentiability assumptions of the data at the point of consideration.

Keywords

Nonsmooth vector optimization necessary optimality conditions weak solutions second-order tangent sets second-order directional derivatives 

Mathematics Subject Classification

90C29 90C46 49K27 26B05 

Notes

Acknowledgments

This work was supported by a grant of the UEH Foundation for Academic Research. The final part of working on the paper was completed during a stay of the author as research visitor at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully acknowledged. The author would like to thank the Editors and Anonymous Referee for their valuable remarks and suggestions, which have helped him to improve the paper.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Economics-Ho Chi Minh CityHo Chi Minh CityVietnam

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