{"paper":{"title":"Approaching nonsmooth nonconvex optimization problems through first order dynamical systems with hidden acceleration and Hessian driven damping terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot","submitted_at":"2016-10-04T09:39:11Z","abstract_excerpt":"In this paper we carry out an asymptotic analysis of the proximal-gradient dynamical system \\begin{equation*}\\left\\{ \\begin{array}{ll} \\dot x(t) +x(t) = \\prox_{\\gamma f}\\big[x(t)-\\gamma\\nabla\\Phi(x(t))-ax(t)-by(t)\\big],\\\\ \\dot y(t)+ax(t)+by(t)=0 \\end{array}\\right.\\end{equation*} where $f$ is a proper, convex and lower semicontinuous function, $\\Phi$ a possibly nonconvex smooth function and $\\gamma, a$ and $b$ are positive real numbers. We show that the generated trajectories approach the set of critical points of $f+\\Phi$, here understood as zeros of its limiting subdifferential, under the pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00911","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"}