{"paper":{"title":"Accelerated Methods for Non-Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.OC","authors_text":"Aaron Sidford, John C. Duchi, Oliver Hinder, Yair Carmon","submitted_at":"2016-11-02T19:58:30Z","abstract_excerpt":"We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(\\epsilon^{-7/4} \\log(1/ \\epsilon) )$ to find an $\\epsilon$-stationary point, meaning a point $x$ such that $\\|\\nabla f(x)\\| \\le \\epsilon$. The method improves upon the $O(\\epsilon^{-2} )$ complexity of gradient descent and provides the additional second-order guarantee that $\\nabla^2 f(x) \\succeq -O(\\epsilon^{1/2})I$ for the computed $x$. Furthermore, our method is Hessian free, i.e. it only requires gradient computations, and is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00756","kind":"arxiv","version":2},"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"}