Abstract:
Distributed optimization is a very important concept with applications in control theory and many related fields, as it is high faulttolerant 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. +us, it gives us an opportunity to analyze distributed optimization techniques that is demanded in most distributed optimization settings. +is 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. +ese 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.
