A newton based distributed optimization method with local interactions for large-scale networked optimization problems

One of the important challenges in the large-scale networked systems is the evaluation of its optimal point of operation. The problem becomes essentially challenging in large-scale networks due to high-dimensionality of the problem, lack of global information, and uncertain and dynamic nature of the operation. The inadequacies of the traditional centralized optimization techniques in addressing these issues have prompted the researchers to investigate distributed optimization techniques. In this paper, an effort has been made to develop a Newton based distributed interior point optimization method to address some of the different issues in the field of distributed optimization. Distributed optimization methods are typically iterative methods, and the approach used in this paper focuses on the generation of both primal and dual feasible solutions at each iteration and the development of mechanisms so that the system can perform only with local information. The paper carries out an analysis of the convergence of both the primal and dual variables in the system. Numerical simulation results for Network Utility Maximization (NUM) problem are provided in this paper as well as a comparison between the proposed distributed and centralized method of optimization is carried out to evaluate the performance of the proposed method.