Robust spherical separation

We propose a robust spherical separation technique aimed at separating two finite sets of points (Formula presented.) and (Formula presented.). Robustness concerns the possibility to admit uncertainties and perturbations in the data-set, which may occur when the data are corrupted by noise or are influenced by measurement errors. In particular, starting from the standard spherical separation under the assumption of spherical uncertainty, we propose a model characterized by a non-convex non-differentiable objective function, which we minimize by means of a bundle-type algorithm. Quite promising numerical results are provided on small and large data-sets drawn from well-established test beds in literature.