Monotonicity of metric projection onto positive cones of ordered Euclidean spaces (Q1063820)

Let \(\pi\) denote the metric projection onto the closed proper convex cone K in \(R^ n\) with vertex at the origin. The necessary and sufficient condition in order to have \(\pi\) (v)-\(\pi\) (u)\(\in K\) whenever v-u\(\in K\) is that any two distinct extreme rays of the polar cone \(K^ 0\) of K form an obtuse angle.