  We give a general proof of convergence for the Alternating Direction Method
of Multipliers (ADMM). ADMM is an optimization algorithm that has recently
become very popular due to its capabilities to solve large-scale and/or
distributed problems. We prove that the sequence generated by ADMM converges to
an optimal primal-dual optimal solution. We assume the functions f and g,
defining the cost f(x) + g(y), are real-valued, but constrained to lie on
polyhedral sets X and Y. Our proof is an extension of the proofs from
[Bertsekas97, Boyd11].
