, Volume 16, Issue 3, pp 311–337 | Cite as

Optimality and duality in constrained interval-valued optimization

  • Do Van LuuEmail author
  • Tran Thi Mai
Research Paper


Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.


Interval-valued optimization problems Local LU-optimal solutions Fritz John and Karush–Kuhn–Tucker optimality conditions Convexificators Asymptotic pseudoconvexity Asymptotic quasiconvexity Duality 

Mathematics Subject Classification

90C46 90C29 49J52 



The author is grateful to the referees for their valuable comments and suggestions which improve the paper.


This study was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.301.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.TIMASThang Long UniversityHanoiVietnam
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  3. 3.Thai Nguyen University of Economics and Business AdministrationThai NguyenVietnam

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