{"paper":{"title":"Network Newton-Part II: Convergence Rate and Implementation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alejandro Ribeiro, Aryan Mokhtari, Qing Ling","submitted_at":"2015-04-23T01:28:49Z","abstract_excerpt":"The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the corresponding Hessian is sparse, and approximate the Newton step by truncating a Taylor expansion of the inverse Hessian. Truncating the series at $K$ terms yields the NN-$K$ that requires aggregating information from $K$ hops away. Network Newton is introduced and shown to converge to the solution of the penalized objective function at a rate that is at lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06020","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"}