The generalization of total ordering cones and vectorization to separable Hilbert spaces
Journal of Mathematical Analysis and Applications, cilt.389, sa.2, ss.1344-1351, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 389 Sayı: 2
- Basım Tarihi: 2012
- Doi Numarası: 10.1016/j.jmaa.2012.01.017
- Dergi Adı: Journal of Mathematical Analysis and Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1344-1351
- Anahtar Kelimeler: Set-valued optimization, Vector optimization, Total ordering cone, Separable Hilbert space, Scalarization
- Uşak Üniversitesi Adresli: Evet
Özet
The characterization of total ordering cones of Rn was given with some properties and optimality conditions in Küçük et al. (2011) [1]. In addition, total ordering cones were used to derive a vector valued function from a special class of set valued mappings in Küçük et al. (2012) [2]. In this study, we give a method for construction of a total ordering cone in a separable Hilbert space by using an orthogonal base. Moreover, we show that every total order can be represented by such a cone. The relationship between the notion of total ordering cone and the notion of vectorization of some set valued mappings are given and some results are obtained. © 2012 Elsevier Inc.