{"paper":{"title":"A dynamic approach to a proximal-Newton method for monotone inclusions in Hilbert spaces, with complexity O(1/n^2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Benar F. Svaiter, Hedy Attouch, Maicon Marques Alves","submitted_at":"2015-02-15T07:07:51Z","abstract_excerpt":"In a Hilbert setting, we introduce a new dynamical system and associated algorithms for solving monotone inclusions by rapid methods.\n  Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I + \\lambda(t) {A})^{-1}$, where the positive control parameter $\\lambda(t)$ tends to infinity as $t \\to + \\infty$. The tuning of $ \\lambda (\\cdot) $ is done in a closed-loop way, by resolution of the algebraic equation $\\lambda \\norm{(I + \\lambda {A})^{-1}x -x}=\\theta$, where $\\theta $ is a positive given constant. The existence and uniqueness of a strong glob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04286","kind":"arxiv","version":2},"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"}