{"paper":{"title":"Second order dynamical systems associated to variational inequalities","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":"2015-12-15T10:04:29Z","abstract_excerpt":"We investigate the asymptotic convergence of the trajectories generated by the second order dynamical system $\\ddot x(t) + \\gamma\\dot x(t) + \\nabla \\phi(x(t))+\\beta(t)\\nabla \\psi(x(t))=0$, where $\\phi,\\psi:{\\cal H}\\rightarrow \\R$ are convex and smooth functions defined on a real Hilbert space ${\\cal H}$, $\\gamma>0$ and $\\beta$ is a function of time which controls the penalty term. We show weak convergence of the trajectories to a minimizer of the function $\\phi$ over the (nonempty) set of minima of $\\psi$ as well as convergence for the objective function values along the trajectories, provided"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04702","kind":"arxiv","version":3},"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"}