A vectorization for nonconvex set-valued optimization
TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.4, ss.1815-1832, 2018 (SCI-Expanded, Scopus, TRDizin)
- 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: Set-valued optimization, nonconvex optimization, vectorization, optimality conditions, TOTAL ORDERING CONES, VECTOR OPTIMIZATION, CONJUGATE DUALITY, SCALARIZATION, MAPS, RESPECT
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Anadolu 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.