Monotonic Optimization in Communication and Networking Systems

Abstract

Optimization has been widely used in recent design of communication and networking systems. One major hurdle in this endeavor lies in the nonconvexity of many optimization problems that arise from practical systems. To address this issue, we observe that most nonconvex problems encountered in communication and networking systems exhibit monotonicity or hidden monotonicity structures. A systematic use of the monotonicity properties would substantially alleviate the difficulty in obtaining the global optimal solutions of the problems. This monograph provides a succinct and accessible introduction to monotonic optimization, including the formulation skills and solution algorithms. Through several application examples, we will illustrate modeling techniques and algorithm details of monotonic optimization in various scenarios. With this promising technique, many previously difficult problems can now be solved with great efficiency. With this monograph, we wish to spur new research activities in broadening the scope of application of monotonic optimization in communication and networking systems.