A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features

Abstract

By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known alternating direction method of multipliers (ADMM) has turned out to be one of the most popular tools for distributed optimization due to many advantages, such as modular structure, superior convergence, easy implementation and high flexibility. In the past decade, ADMM has experienced widespread developments. The developments manifest in both handling more general problems and enabling more effective implementation. Specifically, the method has been generalized to broad classes of problems (i.e., multi-block, coupled objective, nonconvex, etc.). Besides, it has been extensively reinforced for more effective implementation, such as improved convergence rate, easier subproblems, higher computation efficiency, flexible communication, compatible with inaccurate information, robust to communication delays, etc. These developments lead to a plentiful of ADMM variants to be celebrated by broad areas ranging from smart grids, smart buildings, wireless communications, machine learning and beyond. However, there lacks a survey to document those developments and discern the results. To achieve such a goal, this paper provides a comprehensive survey on ADMM variants. Particularly, we discern the five major classes of problems that have been mostly concerned and discuss the related ADMM variants in terms of main ideas, main assumptions, convergence behaviors and main features. In addition, we figure out several important future research directions to be addressed. This survey is expected to work as a tutorial for both developing distributed optimization in broad areas and identifying existing research gaps.

Imitation of Manipulation Skills Using Multiple Geometries

“…Also, ADMM is typically less dependent on parameter settings than many other distributed methods and, therefore, is easy to implement. Overall, ADMM can often offer performance comparable to specialized algorithms, and in most cases, the simple ADMM algorithm will be efficient enough to be useful in many robotics problems [20], see Yang et al [43] for a comprehensive survey on the fundamental property and optimization options in ADMM. In robot manipulation tasks, it has also been used in contact-rich optimization problems.…”

Effect of modelling choices in the unit commitment problem

“…The recent resurgence of interest in alternating direction method of multipliers (ADMM) Yang et al [2022] have also resulted in an increased application of augmented Lagrangian methods, such as ADMM, to the UC Feizollahi et al [2015], Kraning et al [2014], Ramanan et al [2017], Zhang and Hedman [2021], Xavier et al [2020].…”