The generalization of total ordering cones and vectorization to separable Hilbert spaces

Kucuk M., Soyertem M., KÜÇÜK Y.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.389, no.2, pp.1344-1351, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 389 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.1016/j.jmaa.2012.01.017
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1344-1351
  • Keywords: Set-valued optimization, Vector optimization, Total ordering cone, Separable Hilbert space, Scalarization, VALUED OPTIMIZATION PROBLEMS
  • Anadolu University Affiliated: Yes

Abstract

The characterization of total ordering cones of R-n was given with some properties and optimality conditions in Kucuk et al. (2011) W. In addition, total ordering cones were used to derive a vector valued function from a special class of set valued mappings in Kucuk 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. (C) 2012 Elsevier Inc. All rights reserved.