Institute of Electrical & Electronic Engineers
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 non-convex function that satisfies tightness and differentiation conditions. Moreover, a way is introduced to generalize that CUBA by incorporating a convex function.