Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on distributed optimization applied to multi-robot problems. In this paper, we survey three main classes of distributed optimization algorithms -- distributed first-order methods, distributed sequential convex programming methods, and alternating direction method of multipliers (ADMM) methods -- focusing on fully-distributed methods that do not require coordination or computation by a central computer. We describe the fundamental structure of each category and note important variations around this structure, designed to address its associated drawbacks. Further, we provide practical implications of noteworthy assumptions made by distributed optimization algorithms, noting the classes of robotics problems suitable for these algorithms. Moreover, we identify important open research challenges in distributed optimization, specifically for robotics problems.

翻译：尽管分布式优化领域已较为成熟，但专注于分布式优化在多机器人问题中应用的文献仍然有限。本综述是分布式优化应用于多机器人问题系列研究的第二部分。本文系统评述了三大类分布式优化算法——分布式一阶方法、分布式序列凸规划方法以及交替方向乘子法（ADMM）方法，重点关注无需中央计算机协调或计算的完全分布式方法。我们阐述了各类方法的基本架构，并指出了围绕该架构设计的重要变体及其针对相应缺陷的改进思路。此外，我们分析了分布式优化算法中若干重要假设的实际影响，指明了适用于这些算法的机器人问题类别。最后，我们指出了分布式优化领域，特别是面向机器人应用时，亟待解决的重要开放性研究挑战。