More often than not, engineering optimization problems are nonlinear and nonconvex and large in terms of the number of variables and constraints. These two characteristics render off-the-shelf solution techniques (and the solvers that implement them) generally useless. On one hand, relaxation techniques in optimization seek to reduce the complexity resulting from nonconvex nonlinearities by convexifying, linearizing, or simply ignoring certain not-that-relevant constraints. On the other hand, decomposition procedures seek to solve a large optimization problem by breaking it into small subproblems within an iterative process. The combination of relaxation and decomposition often allows solving large-scale nonlinear and nonconvex engineering optimization problems effectively and accurately, and this is the focus of this monograph.