{"paper":{"title":"A Proof of Convergence For the Alternating Direction Method of Multipliers Applied to Polyhedral-Constrained Functions","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jo\\~ao F. C. Mota, Jo\\~ao M. F. Xavier, Markus P\\\"uschel, Pedro M. Q. Aguiar","submitted_at":"2011-12-10T18:39:09Z","abstract_excerpt":"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]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2295","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}