{"paper":{"title":"Fast primal-dual methods for convex-concave bilinear saddle point problems: continuous-time dynamics and discrete algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin He, Ya-Ping Fang","submitted_at":"2026-06-17T06:03:49Z","abstract_excerpt":"This paper studies Nesterov accelerated methods for continuously differentiable convex-concave bilinear saddle point problems. For the continuous-time model, we analyze a second-order primal-dual dynamical system with vanishing damping $\\alpha/t$, where $\\alpha\\geq 3$. Under the merely convex-concave setting, we prove convergence of the primal-dual trajectory to a saddle point. In the noncritical regime $\\alpha>3$, we further obtain the improved rate $o(1/t^{2})$ for the primal-dual gap and $o(1/t)$ for the velocity, and, under an additional Lipschitz gradient assumption, $o(1/t)$ for the stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18724","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/2606.18724/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"}