A novel class of iterative approximation methods for DSL spectrum optimization

Spectrum optimization is a promising means to tackle the crosstalk problem in DSL systems, and corresponds to a challenging nonconvex optimization problem. Iterative convex approximation (ICA) methods have been proposed in the literature to deal with this optimization problem. These methods consist in solving a series of improving convex approximations and are typically implemented in a per-user iterative approach. In this paper we develop a novel class of iterative methods that focus explicitly on per-user iterative implementations, and which consist of improved per-user approximations that are tighter and simpler to solve (in closed-form) than state-of-the-art ICA methods. As a result, the proposed methods improve the convergence speed as fewer approximations are required to converge, and display a significantly lower computational cost. Furthermore, three of the proposed methods can tackle the issue of getting stuck in bad locally optimal solutions, and hence improve solution quality with respect to existing ICA methods.