{"paper":{"title":"Newton-like dynamics associated to nonconvex optimization problems","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":"2017-03-03T21:03:09Z","abstract_excerpt":"We consider the dynamical system \\begin{equation*}\\left\\{ \\begin{array}{ll} v(t)\\in\\partial\\phi(x(t))\\\\ \\lambda\\dot x(t) + \\dot v(t) + v(t) + \\nabla \\psi(x(t))=0, \\end{array}\\right.\\end{equation*} where $\\phi:\\R^n\\to\\R\\cup\\{+\\infty\\}$ is a proper, convex and lower semicontinuous function, $\\psi:\\R^n\\to\\R$ is a (possibly nonconvex) smooth function and $\\lambda>0$ is a parameter which controls the velocity. We show that the set of limit points of the trajectory $x$ is contained in the set of critical points of the objective function $\\phi+\\psi$, which is here seen as the set of the zeros of its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01339","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"}