{"paper":{"title":"Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin He, Ya-Ping Fang","submitted_at":"2025-09-10T03:32:14Z","abstract_excerpt":"In this paper, we study a bilinear saddle point problem of the form $\\min_{x}\\max_{y} F(x) + \\langle Ax, y \\rangle - G(y)$, where $F$ and $G$ are $\\mu_F$- and $\\mu_G$-strongly convex functions, respectively. By incorporating Nesterov acceleration for strongly convex optimization, we first propose an optimal first-order discrete primal-dual gradient algorithm. We show that it achieves the optimal convergence rate $\\mathcal{O}\\left(\\left(1 - \\min\\left\\{\\sqrt{\\frac{\\mu_F}{L_F}}, \\sqrt{\\frac{\\mu_G}{L_G}}\\right\\}\\right)^k\\right)$ for both the primal-dual gap and the iterative, where $L_F$ and $L_G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08258","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/2509.08258/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"}