Monotonic Optimization for Communication and Networking Systems
Optimization techniques have found wide application in designing efficient algorithms that approach the utmost performance of communication and networking systems. Most recent advances in this regard rely crucially on the convexity of the problem formulation. Nonetheless, many problems encountered in practical systems are non-convex by their very nature. These problems are not only non-convex in their original forms, but also cannot be equivalently transformed to convex ones by any existing means. One such example is power control for throughput maximization in wireless interference channels.
An encouraging observation, however, is that a majority of non-convex problems encountered in communication and networking systems exhibit monotonicity or hidden monotonicity structures. A systematic use of monotonicity properties may substantially alleviate the difficulty in obtaining the global optimal solution(s) of the problems, and this is indeed the key idea behind the Monotonic Optimization theory. In this talk, I will introduce the theory and algorithm of Monotonic Optimization. Together with examples of practical applications, I will illustrate the formulation skills of Monotonic Optimization.
Our work on this topic started in 2007 when my student Liping Qian decided to work on the hard problem of wireless power control. We then extended the work to link scheduling, MIMO beamforming, and random access control. Very recently, we published a monograph with exactly the same title of this talk. I look forward to discussing with you on the potential applications of this useful tool.