Advertisement

Positivity

, Volume 20, Issue 2, pp 295–298 | Cite as

A note on “Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality” [Positivity. 18, 449–473(2014)]

  • Xu YihongEmail author
  • Li Min
  • Peng Zhenhua
Article

Abstract

The note points out that the sufficiency of proposition 2.1 in Anh (Positivity 18:449–473, 2014) is erroneous and we provide an example to illustrate it. Also the proof of proposition 2.2 in Anh (Positivity 18:449–473, 2014) is incorrect and we give a new proof.

Keywords

Generalized subconvexlike Convex cone Set-valued map 

Mathematics Subject Classification

32F17 46G05 90C29 90C46 

References

  1. 1.
    Yang, X.M., Yang, X.Q., Chen, G.Y.: Theorems of the alternative and optimization with set-valued maps. J. Optim. Theory Appl. 107, 627–640 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Yang, X.M., Li, D., Wang, S.Y.: Near-subconvexlikeness in vector optimization with set-valued functions. J.Optim. Theory Appl. 110, 413–427 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Sach, P.H.: New generalized convexity notion for set-valued maps and application to vector optimization. J. Optim. Theory Appl. 125, 157–179 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Xu, Yihong: Song, Xiaoshuai: Relationship between ic-cone-convexness and nearly cone-subconvexlikeness. Appl. Math. Lett. 24, 1622–1624 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Anh, N.L.H.: Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18, 449–473 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsNanchang UniversityNanchangChina

Personalised recommendations