Set Containment Characterization

نویسنده

  • Olvi L. Mangasarian
چکیده

Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classifiers [7], is extended to the following: (i) Containment of one polyhedral set in another. (ii) Containment of a polyhedral set in a reverse-convex set defined by convex quadratic constraints. (iii) Containment of a general closed convex set, defined by convex constraints, in a reverse-convex set defined by convex nonlinear constraints. The first two characterizations can be determined in polynomial time by solving m linear programs for (i) and m convex quadratic programs for (ii), where m is the number of constraints defining the containing set. In (iii), m convex programs need to be solved in order to verify the characterization, where again m is the number of constraints defining the containing set. All polyhedral sets, like the knowledge sets of support vector machine classifiers, are characterized by the intersection of a finite number of closed halfspaces.

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عنوان ژورنال:
  • J. Global Optimization

دوره 24  شماره 

صفحات  -

تاریخ انتشار 2002