A vectorization for nonconvex set-valued optimization

Karaman E., Güvenç I. A., SOYERTEM M., Tozkan D., Küçük M., Küçük Y.

Turkish Journal of Mathematics, cilt.42, sa.4, ss.1815-1832, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1707-75
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1815-1832
  • Anahtar Kelimeler: Nonconvex optimization, Optimality conditions, Set-valued optimization, Vectorization
  • Uşak Üniversitesi Adresli: Evet

Özet

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.