Discrepancy norm: Approximation and variations

This paper introduces an approach for the minimization of the discrepancy norm. The general idea is to replace the infinity norms appearing in the definition by LpLp norms which are differentiable and to make use of this approximation for local optimization.We will show that the discrepancy norm can be approximated up to any εε and the robustness of this approximation is shown. Moreover, analytical formulation of the derivative of the discrepancy correlation function is given.In a following step we extend the results to higher dimensional data and derive the related forms for approximations and differentiations.