Journal of Global Optimization

, Volume 75, Issue 1, pp 131–141 | Cite as

Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem

  • M. Chinaie
  • F. Fakhar
  • M. FakharEmail author
  • H. R. Hajisharifi


In this paper, we characterize the nonemptiness of the set of weak minimal elements for a nonempty subset of a linear space. Moreover, we obtain some existence results for a nonconvex set-valued optimization problem under weaker topological conditions.


Algebraic interior Linear space Set-valued optimization Vector closure 



The authors would like to thank the associate editor and reviewers for their constructive comments, which helped us to improve the paper. We also thank Professor Nicolas Hadjisavvas and Professor Constantin Zalinescu who read our manuscript and provided us with valuable comments. The third and fourth authors were partially supported by a Grant from IPM (Nos. 96550414, 98460038).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • M. Chinaie
    • 1
  • F. Fakhar
    • 1
  • M. Fakhar
    • 1
    • 3
    Email author
  • H. R. Hajisharifi
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran
  2. 2.Department of MathematicsUniversity of KhansarKhansarIran
  3. 3.School of MathematicsInstitute for Research in Fundamental SciencesTehranIran

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