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dc.contributor.authorMangasarian, Olvi
dc.date.accessioned2013-01-17T17:34:17Z
dc.date.available2013-01-17T17:34:17Z
dc.date.issued2001
dc.identifier.citation01-10en
dc.identifier.urihttp://digital.library.wisc.edu/1793/64310
dc.description.abstractCharacterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classi ers [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 de ned by convex quadratic constraints. (iii) Containment of a general closed convex set, de ned by convex constraints, in a reverse-convex set de ned by convex nonlinear constraints. The rst 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 de ning 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 de ning the containing set. All polyhedral sets, like the knowledge sets of support vector machine classi ers, are characterized by the intersection of a nite number of closed halfspaces.en
dc.subjectquadratic programmingen
dc.subjectlinear programmingen
dc.subjectknowledge-based classifieren
dc.subjectset containmenten
dc.titleSet Containment Characterizationen
dc.typeTechnical Reporten


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    DMI Technical Reports Archive for the Department of Computer Sciences at the University of Wisconsin-Madison

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