Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Next Article

Journal of Convex Analysis 21 (2014), No. 1, 001--028
Copyright Heldermann Verlag 2014

Conic Separation of Finite Sets. I: The homogeneous case

Annabella Astorino
Istituto di Calcolo e Reti ad Alte Prestazioni C.N.R., UniversitÓ della Calabria, 87036 Rende, Italy

Manlio Gaudioso
Dip. di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, UniversitÓ della Calabria, 87036 Rende, Italy

Alberto Seeger
Dept. of Mathematics, University of Avignon, 33 rue Louis Pasteur, 84000 Avignon, France


This work addresses the issue of separating two finite sets in $\mathbb{R}^n$ by means of a suitable revolution cone $$ \Gamma (z,y,s)= \{x \in \mathbb{R}^n : s\,\Vert x-z\Vert - y^T(x-z)=0\}. $$ The specific challenge at hand is to determine the aperture coefficient $s$, the axis $y$, and the apex $z$ of the cone. These parameters have to be selected in such a way as to meet certain optimal separation criteria. Part I of this work focusses on the homogeneous case in which the apex of the revolution cone is the origin of the space. The homogeneous case deserves a separated treatment, not just because of its intrinsic interest, but also because it helps to built up the general theory. Part II of this work concerns the non-homogeneous case in which the apex of the cone can move in some admissible region. The non-homogeneous case is structurally more involved and leads to challenging nonconvex nonsmooth optimization problems.

Keywords: Conical separation, revolution cone, convex optimization, DC-optimization, proximal point techniques, classification.

MSC: 90C25, 90C26

[ Fulltext-pdf  (214  KB)] for subscribers only.