Optimality conditions in set-valued optimization problem with respect to a partial order relation via directional derivative

Karaman E., SOYERTEM M., Güvenç İ. A.

Taiwanese Journal of Mathematics, vol.24, no.3, pp.709-722, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.11650/tjm/190604
  • Journal Name: Taiwanese Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.709-722
  • Keywords: Directional derivative, Optimality conditions, Partial order, Set-valued optimization
  • Uşak University Affiliated: Yes

Abstract

In this study, a new directional derivative is defined by using Minkowski difference. Some properties and existence theorems of this directional derivative are given. Moreover, necessary and sufficient optimality conditions are presented for set-valued optimization problems with respect to m1 order relation via directional derivative.