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 problem.

翻译：尽管分布式优化领域已较为成熟，但专注于将分布式优化应用于多机器人问题的相关文献仍较为有限。本综述是关于分布式优化在多机器人问题中应用的两部分系列文章的第二部分。本文综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）——重点聚焦于无需中央计算机协调或计算的完全分布式方法。我们描述了每类方法的基本结构，并指出了围绕该结构的、旨在解决其相关缺陷的重要变体。此外，我们还探讨了分布式优化算法所做出的关键假设的实际意义，并指出了适用于这些算法的机器人问题类别。同时，我们识别了分布式优化领域（特别是针对机器人问题）中重要的开放性研究挑战。