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 article, we survey three main classes of distributed optimization algorithms—distributed first-order (DFO) 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.