The multi-carrier Interference channel where interference is treated as additive white Gaussian noise, is a very active topic of research, particularly important in the area of Dynamic Spectrum Management (DSM) for Digital Subscriber Lines (DSL). Here, multiple users optimize their transmit power spectra so as to maximize the total weighted sum of data rates. The corresponding optimization problem is however nonconvex and thus computationally intractable, i.e. a certificate of global optimality requires exponential time complexity algorithms. This paper shows that under certain channel conditions, this nonconvex problem can be solved in polynomial time with a certificate of global optimality. The channel conditions are discussed consisting of different interference models including synchronous and asynchronous DSL transmission. Simulations demonstrate its applicability to realistic DSL scenarios.