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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. [ABSTRACT FROM AUTHOR]

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]