A Proof of Convergence For the Alternating Direction Method of Multipliers Applied to Polyhedral-Constrained Functions
Optimization and Control
2011-12-13 v1
Abstract
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].
Keywords
Cite
@article{arxiv.1112.2295,
title = {A Proof of Convergence For the Alternating Direction Method of Multipliers Applied to Polyhedral-Constrained Functions},
author = {João F. C. Mota and João M. F. Xavier and Pedro M. Q. Aguiar and Markus Püschel},
journal= {arXiv preprint arXiv:1112.2295},
year = {2011}
}