On the performance of distributed algorithms for network optimization problems

This thesis considers optimization problems defined over a network of nodes, where each node knows only part of the objective functions. We are motivated by broad applications of these problems within engineering and sciences, where problems are characterized by either complex networks with a large number of nodes or massive amounts of data. Algorithms for solving these problems should be implemented in parallel between the nodes, and are based only on local computation and communication, necessitating the development of distributed algorithms. Our interest, therefore, is to study distributed methods for solving networked optimization problems, where our focus is on distributed gradient algorithms. In particular, we move beyond the existing results to significantly enhance the performance and reduce the complexity of distributed gradient methods, while taking practical issues, such as communication delays and resource uncertainty, into account. Our goal is to bridge the gap between theory and practice, leading to significant improvement in their performance for solving real-world problems. The remainder of this thesis is to focus on three main thrusts --- first, we study the impact of communication delays, an inevitable issue in distributed systems, on the performance of distributed gradient algorithms. Our results address a notable omission in the existing literature, where the delays are often ignored. Second, we study different variants of distributed gradient algorithms, and show that under certain conditions we can improve their convergence. Finally, we study an important problem within engineering and computer science, namely, network resource allocation. For solving this problem, we propose distributed Lagrangian methods and show that our methods are robust to resource uncertainty. In addition, we design a novel algorithm, namely, the distributed gradient balancing protocol, for solving a special case of network resource allocation problems. We show that our algorithm achieves a quadratic convergence time, which improves the convergence of the existing algorithms by a factor of n, the size of the network

A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning

In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity and implementation issues. For each of the approaches, the problem setup, the general solution and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multi-hop routing designs in general multi-hop networks are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201