Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Separating hyperplane theorem

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_938

Let C1 and C2 by two nonempty disjoint convex sets in n-dimensional space. Then there exists an n-dimensional hyperplane axv = b, av ≠ 0, that separates them. That is, for xv in C1, axv ≤ b,v and for xv in C2, axv ≥ b.v  Hyperplane.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA