Let $P$ be a finite set of points in $\mathbb{R}^d$(none of which is zero). In solving certain convex optimization problem, I came up with the following vector
$\hat{x} = \frac{A(P)}{\vert\vert A(P)\vert\vert}$, where $A(P) = \sum_{p\in P}\vert\vert p\vert\vert p$. This is a quite nice looking expression. Does this have any special name, or any special properties?
One thing to note is that, if all the points have unit norm, then $A(P) = n\mu(P)$, where $\mu(P) = \frac{\sum_{p\in P}p}{n}$ is the "mean" of $P$.
Thanks