Successive convex approximation based methods for dynamic spectrum management

This paper contains two parts. The first part presents a novel framework for the successive convex approximation (SCA) method to solve a general optimization problem, as well as its properties. This framework starts with making change of variables (COV), motivated by the fact that it might be easier to construct convex approximations for the problem after making the COV. Furthermore, a general method is proposed to construct a convex upper bound approximation (CUBA) for a nonconvex function that satisfies tightness and differentiation conditions. Moreover, a way is introduced to generalize that CUBA by incorporating a convex function. These methods lead to plenty of degrees of freedom for using the SCA method to solve a problem. The second part revisits state-of-the-art dynamic spectrum management (DSM) algorithms, namely the successive convex approximations for low-complexity (SCALE) algorithm, the convex approximation for distributed spectrum balancing (CA-DSB) algorithm and the difference-of-convex-functions algorithm based DSM (DCA-DSM) method, to show how they can be derived from the SCA and CUBA construction methods. Numerical experiments are shown to compare them.