Wat is Alternating direction method of multipliers?

The alternating direction method of multipliers (ADMM) minimises $f(x) + g(z)$ subject to $x = z$ by alternating $x \leftarrow \operatorname{prox}_{f/\rho}(z - u)$, $z \leftarrow \operatorname{prox}_{g/\rho}(x + u)$, $u \leftarrow u + x - z$ (Boyd, Parikh, Chu, Peleato and Eckstein, 2011).