On the Solidness of the Polar of Recession Cones

Authors: Sima Hassankhali, Ildar Sadeqi

Abstract:

In the theory of Pareto efficient points, the existence of a bounded base for a cone K of a normed space X is so important. In this article, we study the geometric structure of a nonzero closed convex cone K with a bounded base. For this aim, we study the structure of the polar cone K# of K. Furthermore, we obtain a necessary and sufficient condition for a nonempty closed convex set C so that its recession cone C∞ has a bounded base.

Keywords: solid cones, recession cones, polar cones, bounded base