{"paper":{"title":"Inertial Primal Dual Dynamics with Hessian-driven Damping for Smooth and Bilinearly Coupled Saddle Point Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Juan Peypouquet, Zepeng Wang","submitted_at":"2026-07-28T20:15:41Z","abstract_excerpt":"Featuring Hessian-driven damping, two inertial primal dual dynamical systems are proposed for solving smooth saddle point problems with bilinear coupling. For convex-concave functions, we establish a convergence rate $\\mathcal{O}\\left( \\frac{1}{t^2} \\right)$ for the primal dual gap; for strongly convex-strongly concave functions, we obtain an asymptotic rate $\\mathcal{O}\\left( \\frac{1}{t^{\\alpha-1}} \\right)$ ($\\alpha\\ge 3$ is the damping parameter) without knowledge of the strong convexity parameters, and an accelerated linear convergence rate when the strong convexity parameters are known. As"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26235","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/2607.26235/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"}