Non-convex optimization and resource allocation in communication networks

Jang Won Lee, Purdue University

Abstract

In the past few years, utility and optimization based resource allocation problems have been studied by many researchers. These studies have shed important insights on how to design and control both wireless and wireline networks. However, most works have focused on a convex optimization framework that considers only concave utility functions, or a non-cooperative game that converges to inefficient Nash equilibria. In real networks, there exist services that are best represented by non-concave utility functions such as delay and rate sensitive services in the Internet and all services in wireless networks. Thus, previous approaches could lead to inefficient resource allocation and network instability. This necessitates the development of network algorithms that can efficiently handle non-concave utility functions. In this dissertation, we study various problems for resource allocation in communication networks under a rigorous non-convex optimization framework. We develop simple algorithms for efficient and fair allocation of resources taking into account the unique characteristics of the different systems being considered. In wireless systems, we investigate the problems dealing with the downlink channel, such as power allocation, joint power and rate allocation, base-station assignment, and multi-server opportunistic scheduling. In addition to developing simple algorithms, we are also able to show fundamental properties that provide insight on how to design optimal resource allocation techniques for wireless systems. We also investigate the rate control problem in the Internet. We show that existing distributed algorithms designed for services with concave utility functions cause instability and congestion in the presence of services with non-concave utility functions. We then develop a distributed algorithm with the property that prices “self-regulate” users to decide whether or not to transmit data based on their net utility, and show that the algorithm converges to an asymptotically optimal rate allocation without causing congestion in the system.

Degree

Ph.D.

Advisors

Shroff, Purdue University.

Subject Area

Electrical engineering

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