Polyhedral separability through successive LP

  • Authors:
  • A. Astorino;M. Gaudioso

  • Affiliations:
  • Researcher, Istituto per la Sistemistica e l'Informatica, ISI CNR, Rende, Cosenza, Italia;Professor, Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, Rende, Cosenza, Italia

  • Venue:
  • Journal of Optimization Theory and Applications
  • Year:
  • 2002

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Abstract

We address the problem of discriminating between two finite point sets A and B in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of A with B is empty, the two sets can be strictly separated (polyhedral separability). We introduce an error function which is piecewise linear, but not convex nor concave, and define a descent procedure based on the iterative solution of the LP descent direction finding subproblems.