{"paper":{"title":"Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Quoc Tran-Dinh, Yang Luo","submitted_at":"2021-10-15T15:26:32Z","abstract_excerpt":"In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called Halpern-type fixed-point iteration in [32], and recently exploited by a number of researchers, including [24, 70]. Firstly, we derive a new variant of the anchored extra-gradient scheme in [70] based on Popov's past extra-gradient method to solve a maximally monotone equation $G(x) = 0$. We show that our method achieves the same $\\mathcal{O}(1/k)$ convergence rate ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08150","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.08150/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}