A Proof of Convergence For the Alternating Direction Method of Multipliers Applied to Polyhedral-Constrained Functions

Details A Proof of Convergence For the Alternating Direction Method of Multipliers Applied to Polyhedral-Constrained Functions A Proof of Convergence For the Alternating Direction Method of Multipliers Applied to Polyhedral-Constrained Functions

2011-12-10

arxiv.org/abs/1112.2295v1

Mathematics

Optimization and Control

Scientific paper

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].

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