A Study on Distributed Optimization over Large-Scale Networked Systems

Abstract

Distributed optimization is a very important concept with applications in control theory and many related fields, as it is high fault-tolerant and extremely scalable compared with centralized optimization. Centralized solution methods are not suitable for many application domains that consist of large number of networked systems. In general, these large-scale networked systems cooperatively find an optimal solution to a common global objective during the optimization process. Thus, it gives us an opportunity to analyze distributed optimization techniques that is demanded in most distributed optimization settings. This paper presents an analysis that provides an overview of decomposition methods as well as currently existing distributed methods and techniques that are employed in large-scale networked systems. A detailed analysis on gradient like methods, subgradient methods, and methods of multipliers including the alternating direction method of multipliers is presented. These methods are analyzed empirically by using numerical examples. Moreover, an example highlighting the fact that the gradient method fails to solve distributed problems in some circumstances is discussed under numerical results. A numerical implementation is used to demonstrate that the alternating direction method of multipliers can solve this particular problem, by revealing its robustness compared with the gradient method. Finally, we conclude the paper with possible future research directions.

Distributed Optimization of Social Welfare and Regulation in Industrial Economy

“…Its good scalability and fault tolerance can effectively solve complex problems that cannot be solved by other methods. Among them, distributed optimization theory, as one of the important development directions of contemporary systems and control science, has received extensive attention in fields such as wireless sensor networks, machine learning, and cooperative control [17][18][19][20]. Distributed optimization of multi-agent systems is mainly based on the actual problem of distributed optimization modeling as the minimization of a global objective function, that is, the problem is solved on a connected network and distributed by multiple agents as shown in Figure 2.…”