The Surgical Separation of Sets View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1997-12

AUTHORS

James E. Falk, Emma Lopez-Cardona

ABSTRACT

Given a pair of finite disjoint setsA andB inRn, a fundamental problem with many important applications isto efficiently determine a hyperplaneH(w,λ) which separates these sets when they are separable, or ‘nearly’ separates themwhen they are not. We seek a hyperplane which minimizes a natural errormeasure in the latter case, and so will ‘surgically’ separate the sets. Whenthe sets are separable in a strong sense, we show that the problem is aconvex program with a unique solution, which has been investigated byothers. Using the KKT conditions, we improve on an existing algorithm. Whenthe sets are not separable, the problem is nonconvex, generally with properlocal solutions, and we solve an equivalent problem by Branch and Bound.Numerical results are presented. More... »

PAGES

433-462

References to SciGraph publications

  • 1976-06. Infinitely constrained optimization problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1008284015704

    DOI

    http://dx.doi.org/10.1023/a:1008284015704

    DIMENSIONS

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