1. The generalization of total ordering cones and vectorization to separable Hilbert spaces
- Author
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Küçük, Mahide, Soyertem, Mustafa, and Küçük, Yalçın
- Subjects
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VECTOR fields , *SEPARABLE algebras , *HILBERT space , *MATHEMATICAL optimization , *MATHEMATICAL mappings , *ORTHOGONALIZATION , *SET-valued maps - Abstract
Abstract: The characterization of total ordering cones of was given with some properties and optimality conditions in Küçük et al. (2011) . 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) . 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. [Copyright &y& Elsevier]
- Published
- 2012
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