- Conic separation of finite sets: The non-homogeneous case Annabella Astorino(astorinoicar.cnr.it) Manlio Gaudioso(gaudiosodeis.unical.it) Alberto Seeger(alberto.seegeruniv-avignon.fr) Abstract: 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. Keywords: Conical separation, revolution cone, alternating minimization, DC programming, classification. Category 1: Applications -- Science and Engineering Category 2: Convex and Nonsmooth Optimization Citation: 90C26. Download: [PDF]Entry Submitted: 10/14/2013Entry Accepted: 10/14/2013Entry Last Modified: 10/14/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.