Partial order relations on family of sets and scalarizations for set optimization

Karaman E., SOYERTEM M., Atasever Güvenç İ., Tozkan D., Küçük M., Küçük Y.

Positivity, cilt.22, sa.3, ss.783-802, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s11117-017-0544-3
  • Dergi Adı: Positivity
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.783-802
  • Anahtar Kelimeler: Optimality conditions, Partial order, Scalarization, Set optimization
  • Uşak Üniversitesi Adresli: Evet

Özet

In this study, some new order relations on family of sets are introduced by using Minkowski difference. The relations between these orders and the ordering cone of the vector space are obtained. It is shown that depending on the corresponding cone, these order relations are partial orders on the family of nonempty bounded sets. Some relationships between these order relations and upper and lower set less order relations are investigated. Also, two scalarizing functions are introduced in order to replace set optimization problems with respect to these partial order relations with scalar optimization problems. Moreover, necessary and sufficient optimality conditions are presented.