Conic Separation of Finite Sets. II: The Non-Homogeneous Case

[For part I of this article see this journal 21 (2013), Number 1.]\par We address the issue of separating two finite sets in $\mathbb{R}^n$ by means of a suitable revolution cone $$\Gamma (z,y,s)= \{x \in \mathbb{R}^n:\, s\,\Vert x-z\Vert - y^T(x-z)=0\}.$$ One has to select the aperture coefficient $s$, the axis $y$, and the apex $z$ in such a way as to meet certain optimal separation criteria. The homogeneous case $z=0$ has been treated in Part I of this work. We now discuss the more general case in which the apex of the cone is allowed to move in a certain region. The non-homogeneous case is structurally more involved and leads to challenging nonconvex nonsmooth optimization problems.