{"paper":{"title":"The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hedy Attouch, Juan Peypouquet","submitted_at":"2015-10-29T15:30:50Z","abstract_excerpt":"The {\\it forward-backward algorithm} is a powerful tool for solving optimization problems with a {\\it additively separable} and {\\it smooth} + {\\it nonsmooth} structure. In the convex setting, a simple but ingenious acceleration scheme developed by Nesterov has been proved useful to improve the theoretical rate of convergence for the function values from the standard $\\mathcal O(k^{-1})$ down to $\\mathcal O(k^{-2})$. In this short paper, we prove that the rate of convergence of a slight variant of Nesterov's accelerated forward-backward method, which produces {\\it convergent} sequences, is act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08740","kind":"arxiv","version":4},"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"}