Abstract--This paper presents efficient multiuser margin optimization algorithms suitable for multicarrier digital subscriber line (DSL) systems using Dynamic Spectrum Management (DSM). The favorable monotonicity and fairness properties of multiuser margin are employed to formulate a box-constrained nonlinear least squares (NLSQ) problem for multiuser margin maximization, which is efficiently solved by using a scaled-gradient trust-region approach with Broyden Jacobian update. Based on this NLSQ formulation, a multiuser harmonized margin (MHM) optimization algorithm for resource allocation is developed. A Newton