conical separation

Conic separation of finite sets:The homogeneous case

  • Annabella Astorino
  • Manlio Gaudioso
  • Alberto Seeger
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , , , ,

    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 … Read more

    Conic separation of finite sets: The non-homogeneous case

  • Annabella Astorino
  • Manlio Gaudioso
  • Alberto Seeger
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , ,

    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 … Read more