{"paper":{"title":"Fast convex optimization via inertial dynamics with Hessian driven damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hedy Attouch, Juan Peypouquet, Patrick Redont","submitted_at":"2016-01-26T17:47:07Z","abstract_excerpt":"We first study the fast minimization properties of the trajectories of the second-order evolution equation $$\\ddot{x}(t) + \\frac{\\alpha}{t} \\dot{x}(t) + \\beta \\nabla^2 \\Phi (x(t))\\dot{x} (t) + \\nabla \\Phi (x(t)) = 0,$$ where $\\Phi:\\mathcal H\\to\\mathbb R$ is a smooth convex function acting on a real Hilbert space $\\mathcal H$, and $\\alpha$, $\\beta$ are positive parameters. This inertial system combines an isotropic viscous damping which vanishes asymptotically, and a geometrical Hessian driven damping, which makes it naturally related to Newton's and Levenberg-Marquardt methods. For $\\alpha\\geq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07113","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":""},"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"}