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Annabella Astorino(astorinoicar.cnr.it) Abstract: This work addresses the issue of separating two finite sets in $\mathbb{R}^n $ by means of a suitable revolution cone $$ \Gamma (z,y,s)= \{x \in \mathbb{R}^n : s\,\Vert xz\Vert  y^T(xz)=0\}.$$ 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 nonhomogeneous case in which the apex of the cone can move in some admissible region. The nonhomogeneous 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. Category 1: Applications  Science and Engineering Category 2: Convex and Nonsmooth Optimization Citation: 90C25, 90C26 Download: [PDF] Entry Submitted: 10/14/2013 Modify/Update this entry  
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