{"paper":{"title":"On Lower Complexity Bounds for Large-Scale Smooth Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.OC","authors_text":"Arkadi Nemirovski, Cristobal Guzman","submitted_at":"2013-07-18T16:29:21Z","abstract_excerpt":"We derive lower bounds on the black-box oracle complexity of large-scale smooth convex minimization problems, with emphasis on minimizing smooth (with Holder continuous, with a given exponent and constant, gradient) convex functions over high-dimensional ||.||_p-balls, 1<=p<=\\infty. Our bounds turn out to be tight (up to logarithmic in the design dimension factors), and can be viewed as a substantial extension of the existing lower complexity bounds for large-scale convex minimization covering the nonsmooth case and the 'Euclidean' smooth case (minimization of convex functions with Lipschitz c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5001","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"}