{"paper":{"title":"Optimal Algorithm with Complexity Separation for Strongly Convex-Strongly Concave Composite Saddle Point Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aleksandr Beznosikov, Alexander Gasnikov, Dmitry Kovalev, Ekaterina Borodich, Georgiy Kormakov","submitted_at":"2023-07-24T17:18:35Z","abstract_excerpt":"In this work, we focuses on the following saddle point problem $\\min_x \\max_y p(x) + R(x,y) - q(y)$ where $R(x,y)$ is $L_R$-smooth, $\\mu_x$-strongly convex, $\\mu_y$-strongly concave and $p(x), q(y)$ are convex and $L_p, L_q$-smooth respectively. We present a new algorithm with optimal overall complexity $\\mathcal{O}\\left(\\left(\\sqrt{\\frac{L_p}{\\mu_x}} + \\frac{L_R}{\\sqrt{\\mu_x \\mu_y}} + \\sqrt{\\frac{L_q}{\\mu_y}}\\right)\\log \\frac{1}{\\varepsilon}\\right)$ and separation of oracle calls in the composite and saddle part. This algorithm requires $\\mathcal{O}\\left(\\left(\\sqrt{\\frac{L_p}{\\mu_x}} + \\sqrt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.12946","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/2307.12946/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"}