The surgical separation of sets

Let A and B be two disjoint, finite sets of vectors in Rⁿ. We determine if there is a hyperplane H (w,γ) which separates these sets. If so, we efficiently compute a hyperplane which ‘optimally’ separates. If no, we compute a hyperplane which minimizes a function reflecting the ‘error’ associated with the mis-classified points. In both cases, the computed hyperplane is invariant under similarity transformations.