{"paper":{"title":"Accelerating Nesterov's Method for Strongly Convex Functions with Lipschitz Gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hao Chen, Xiangrui Meng","submitted_at":"2011-09-27T23:04:31Z","abstract_excerpt":"We modify Nesterov's constant step gradient method for strongly convex functions with Lipschitz continuous gradient described in Nesterov's book. Nesterov shows that $f(x_k) - f^* \\leq L \\prod_{i=1}^k (1 - \\alpha_k) \\| x_0 - x^* \\|_2^2$ with $\\alpha_k = \\sqrt{\\rho}$ for all $k$, where $L$ is the Lipschitz gradient constant and $\\rho$ is the reciprocal condition number of $f(x)$. Hence the convergence rate is $1-\\sqrt{\\rho}$. In this work, we try to accelerate Nesterov's method by adaptively searching for an $\\alpha_k > \\sqrt{\\rho}$ at each iteration. The proposed method evaluates the gradient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6058","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"}