There are 3 points in a plane $(x_1,y_1)$,$(x_2,y_2)$,$(x_3,y_3)$. I am trying to find a solution to the unconstrained minimization problem which is the point $(a,b)$ of least distance between the 3.
$\min F(a,b) = \sum_{i=1}^3 \sqrt{(a-x_i)^2+(b-y_i)^2}$
I am stuck on the first order conditions.
Any help is much appreciated.