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Conic separation of finite sets: The non-homogeneous case

Annabella Astorino(astorino***at***icar.cnr.it)
Manlio Gaudioso(gaudioso***at***deis.unical.it)
Alberto Seeger(alberto.seeger***at***univ-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: 10/14/2013
Entry Accepted: 10/14/2013
Entry Last Modified: 10/14/2013

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