Geometric properties of a parameterized order relation in vector optimization.

In this paper, we discuss some geometrical and topological properties of a parameterized binary order relation. This relation is based on a special set called. We answer the question under which conditions the natural ordering cone ofis a subset of. Moreover, we examine in which cases the setcoincides with a certain half space. Furthermore, we determine the dual set ofand the contingent cone to. [ABSTRACT FROM AUTHOR]