This work addresses the issue of separating two finite sets R^n by means of a suitable revolution cone. The specific challenge at hand is to determine the aperture coefficient , the axis and the apex 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.
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Titolo: | Conic separation of finite sets. I. The homogeneous case |
Autori: | |
Data di pubblicazione: | 2014 |
Rivista: | |
Handle: | http://hdl.handle.net/20.500.11770/139094 |
Appare nelle tipologie: | 1.1 Articolo in rivista |