Exact Solution of -norm and -norm Plane Separation

We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of L_p-norm distances to the plane of points lying on the wrong side of it. We propose a new mixed integer programming formulation for the -norm case, and an implementation of a nonconvex quadratic programming algorithm for the L₂-norm case, based on a branch-and-cut approach. Computational results are reported for several publicly available data sets and larger artificial problems. We also explore the accelerating potential of incorporating heuris- tic bounds in our exact solution approaches.