Conic Quadratic Formulations for Wireless Communications Design

TL;DR

This paper introduces efficient conic quadratic reformulations for solving nonconvex wireless communication problems using successive convex approximation, significantly reducing computational costs compared to existing methods.

Contribution

It proposes numerically efficient transformations that enable iterative solutions of nonconvex problems via conic quadratic optimization, improving computational efficiency.

Findings

Proposed transformations improve computational efficiency.

Numerical results demonstrate faster solutions.

Theoretical analysis confirms reduced complexity.

Abstract

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.