{"paper":{"title":"Second order dynamical systems with penalty terms associated to monotone inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot, Szil\\'ard Csaba L\\'aszl\\'o","submitted_at":"2017-01-18T21:58:01Z","abstract_excerpt":"In this paper we investigate in a Hilbert space setting a second order dynamical system of the form $$\\ddot{x}(t)+\\g(t)\\dot{x}(t)+x(t)-J_{\\lambda(t) A}\\big(x(t)-\\lambda(t) D(x(t))-\\lambda(t)\\beta(t)B(x(t))\\big)=0,$$ where $A:{\\mathcal H}\\toto{\\mathcal H}$ is a maximal monotone operator, $J_{\\lambda(t) A}:{\\mathcal H}\\To{\\mathcal H}$ is the resolvent operator of $\\lambda(t)A$ and $D,B: {\\mathcal H}\\rightarrow{\\mathcal H}$ are cocoercive operators, and $\\lambda,\\beta :[0,+\\infty)\\rightarrow (0,+\\infty)$, and $\\gamma:[0,+\\infty)\\rightarrow (0,+\\infty)$ are step size, penalization and, respectivel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05246","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"}