  As a wide class of resource management problems in wireless communications
are nonconvex and even NP-hard in many cases, finding globally optimal
solutions to these problems is of little practical interest. Towards more
pragmatic approaches, there is a rich literature on iterative methods aiming at
finding a solution satisfying necessary optimality conditions to these
problems. These approaches have been derived under several similar mathematical
frameworks such as inner approximation algorithm, concave-convex procedure,
majorization-minimization algorithm, and successive convex approximation (SCA).
However, a large portion of existing algorithms arrive at a relatively generic
program at each iteration, which is less computationally efficient compared to
a more standard convex formulation. This paper proposes \emph{numerically
efficient} transformations and approximations for SCA-based methods to deal
with nonconvexity in wireless communications design. More specifically, the
central goal is to show that various nonconvex problems in wireless
communications can be iteratively solved by conic quadratic optimization. We
revisit various examples to demonstrate the advantages of the proposed
approximations. Theoretical complexity analysis and numerical results show the
superior efficiency in terms of computational cost of our proposed solutions
compared to the existing ones.
