Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article
 


Journal of Convex Analysis 21 (2014), No. 3, 819--831
Copyright Heldermann Verlag 2014



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

Annabella Astorino
Istituto di Calcolo e Reti ad Alte Prestazioni C.N.R., Dip. di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, UniversitÓ della Calabria, 87036 Rende, Italy
astorino@icar.cnr.it

Manlio Gaudioso
Dip. di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, UniversitÓ della Calabria, 87036 Rende, Italy
gaudioso@dimes.unical.it

Alberto Seeger
Dept. of Mathematics, University of Avignon, 33 rue Louis Pasteur, 84000 Avignon, France
alberto.seeger@univ-avignon.fr



[Abstract-pdf]

[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.

Keywords: Conical separation, revolution cone, alternating minimization, DC programming, classification.

MSC: 90C26

[ Fulltext-pdf  (135  KB)] for subscribers only.