Geodesic
Conic Separation of Finite Sets. II: The Non-Homogeneous Case
Journal of convex analysis, Tome 21 (2014) no. 3, pp. 819-831

Voir la notice de l'article provenant de la source Heldermann Verlag

[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.
Classification : 90C26
Mots-clés : Conical separation, revolution cone, alternating minimization, DC programming, classification 
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     title = {Conic {Separation} of {Finite} {Sets.} {II:} {The} {Non-Homogeneous} {Case}},
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A. Astorino; M. Gaudioso; A. Seeger. Conic Separation of Finite Sets. II: The Non-Homogeneous Case. Journal of convex analysis, Tome 21 (2014) no. 3, pp. 819-831. http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a12/