Optimality and Duality in Nonsmooth Conic Vector Optimization

  • Thai Doan ChuongEmail author
Regular Paper


This article is concerned with a nonsmooth vector optimization problem involving conic constraints. We employ some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of the conic vector optimization problem, where the fuzzy necessary condition and sequential necessary condition are expressed in terms of the Fréchet subdifferential and the exact necessary condition is in terms of the limiting/Mordukhovich subdifferential of the related functions. Sufficient conditions for (weakly) efficient solutions of the underlying problem are also provided by means of introducing the concepts of (strictly) generalized convex vector functions with respect to a cone. In addition, we propose a dual problem to the conic vector optimization problem and explore weak, strong, and converse duality relations between these two problems.


Necessary/sufficient conditions Duality Vector optimization Conic constraints Limiting/Mordukhovich subdifferential 

Mathematics Subject Classification

49K99 65K10 90C29 90C46 



The author would like to thank three anonymous referees for the valuable comments and suggestions.


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Copyright information

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Authors and Affiliations

  1. 1.Optimization and Applications Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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