{"paper":{"title":"A unified convergence bound for conjugate gradient and accelerated gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Sahar Karimi, Stephen A. Vavasis","submitted_at":"2016-05-01T23:15:59Z","abstract_excerpt":"Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\\x_k)-f(\\x^*)$ by a factor of $\\eps\\in(0,1)$ after $k\\ge O(\\sqrt{L/\\ell}\\log(1/\\eps))$ iterations, where $\\ell,L$ are the two parameters of smooth strong convexity. Furthermore, it is known that this is the best possible complexity in the function-gradient oracle model of computation. The method of linear conjugate gradients (CG) also satisfies the same complexity bound in the special case of strongly convex quadratic functions, but in this special case it is faster than the accele"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00320","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"}