{"paper":{"title":"Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\\L}ojasiewicz condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Theodoros G. Tsironis, Vasiliki Mavrogeorgou, Vassilis Apidopoulos","submitted_at":"2025-06-13T12:19:46Z","abstract_excerpt":"In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a {\\L}ojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the {\\L}ojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they suggest a different tuning of the dynamics' damping terms, even in the strongly convex regime. We co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11705","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/2506.11705/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"}