{"paper":{"title":"An Improved Cutting Plane Method for Convex Optimization, Convex-Concave Games and its Applications","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Haotian Jiang, Sam Chiu-wai Wong, Yin Tat Lee, Zhao Song","submitted_at":"2020-04-08T20:56:40Z","abstract_excerpt":"Given a separation oracle for a convex set $K \\subset \\mathbb{R}^n$ that is contained in a box of radius $R$, the goal is to either compute a point in $K$ or prove that $K$ does not contain a ball of radius $\\epsilon$. We propose a new cutting plane algorithm that uses an optimal $O(n \\log (\\kappa))$ evaluations of the oracle and an additional $O(n^2)$ time per evaluation, where $\\kappa = nR/\\epsilon$.\n  $\\bullet$ This improves upon Vaidya's $O( \\text{SO} \\cdot n \\log (\\kappa) + n^{\\omega+1} \\log (\\kappa))$ time algorithm [Vaidya, FOCS 1989a] in terms of polynomial dependence on $n$, where $\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.04250","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.04250/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}