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Positivity

, Volume 20, Issue 1, pp 187–207 | Cite as

Approximate solutions of multiobjective optimization problems

  • Thai Doan Chuong
  • Do Sang KimEmail author
Article

Abstract

This paper provides some new results on approximate Pareto solutions of a multiobjective optimization problem involving nonsmooth functions. We establish Fritz-John type necessary conditions and sufficient conditions for approximate Pareto solutions of such a problem. As a consequence, we obtain Fritz-John type necessary conditions for (weakly) Pareto solutions of the considered problem by exploiting the corresponding results of the approximate Pareto solutions. In addition, we state a dual problem formulated in an approximate form to the reference problem and explore duality relations between them.

Keywords

Approximate solutions Optimality conditions Duality Fuzzy form Mordukhovich/limiting subdifferential Multiobjective optimization 

Mathematics Subject Classification

41A65 49K99 65K10 90C29 90C46 

Notes

Acknowledgments

The authors would like to thank the referees for valuable comments and suggestions.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.Department of Applied MathematicsPukyong National UniversityBusanKorea

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