Distributed Optimization In Networked Systems PDF Download

This work is intended towards the development of distributed optimization methods for large-scale networked systems. The advancement in technological fields such as networking, communication and computing has facilitated the development of networks which are massively large-scale in nature. One of the important challenges in these networked systems is the evaluation of the optimal point of operation of the system. The problem is essentially challenging due to the high-dimensionality of the problem, distributed nature of resources, lack of global information and dynamic nature of operation of most of these systems. The inadequacies of the traditional centralized optimization techniques in addressing these issues have prompted the researchers to investigate distributed optimization techniques. This research work focuses on developing techniques to carry out the global optimization in a distributed fashion that explores the fundamental idea of decomposing the overall optimization problem into a number of sub-problems that utilize limited information exchanged over the network. Inspired by price-based mechanisms, the research develops two methods. First, a distributed optimization method consisting of dual decomposition and update of dual variables in the subgradient direction is developed for some different classes of resource allocation problems. Although this method is easy to implement, it has its own drawbacks. To address some of the drawbacks in distributed optimization, in this dissertation, a Newton based distributed interior point optimization method is developed. The proposed approach, which is iterative in nature, focuses on the generation of feasible solutions at each iteration and development of mechanisms that demand lesser communication. The convergence and rate of convergence of both the primal and the dual variables in the system is also analyzed using a benchmark Network Utility Maximization (NUM) problem followed by numerical simulation results. A comparative study between the proposed distributed and centralized method of optimization is also provided. The proposed distributed optimization techniques have been applied to real world systems such as optimal power allocation in Smart Grid and utility maximization in Cloud Computing systems. Both the problems belong to the class of large-scale complex network problems. In the power grids, the challenges are augmented with the nature of the decision variables, coupling effect in the network, the global constraints in the system, uncertain nature of renewable power generators, and the large-scale distributed nature of the problem. In cloud computing, resources such as memory, processing, and bandwidth are needed to be allocated to a large number of users to maximize the users' quality of experience. Finally, the research focuses on the development of a stochastic distributed optimization method for solving problems with multi-modal cost functions. As opposed to the unimodal function optimization, the widely practiced gradient descent methods fail to reach the global optimum solution when multi-modal cost functions are considered. In this dissertation, an effort is be made to develop a stochastic distributed optimization method that exploits noise based solution update to prevent the algorithm from converging into local optimum solutions. The method is applied to the Network Utility Maximization problem with multi-modal cost functions, and is compared with Genetic Algorithm.