{"paper":{"title":"Combining fast inertial dynamics for convex optimization with Tikhonov regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hedy Attouch, Zaki Chbani","submitted_at":"2016-02-05T10:47:42Z","abstract_excerpt":"In a Hilbert space setting $\\mathcal H$, we study the convergence properties as $t \\to + \\infty$ of the trajectories of the second-order differential equation \\begin{equation*}\n  \\mbox{(AVD)}_{\\alpha, \\epsilon} \\quad \\quad \\ddot{x}(t) + \\frac{\\alpha}{t} \\dot{x}(t) + \\nabla \\Phi (x(t)) + \\epsilon (t) x(t) =0, \\end{equation*} where $\\nabla\\Phi$ is the gradient of a convex continuously differentiable function $\\Phi: \\mathcal H \\to \\mathbb R$, $\\alpha$ is a positive parameter, and $\\epsilon (t) x(t)$ is a Tikhonov regularization term, with $\\lim_{t \\to \\infty}\\epsilon (t) =0$. In this damped inert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01973","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"}