{"paper":{"title":"A Riemannian Proximal Newton-CG Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Wen Huang, Wutao Si","submitted_at":"2024-05-14T07:05:37Z","abstract_excerpt":"Recently, a Riemannian proximal Newton method has been developed for optimizing problems in the form of $\\min_{x\\in\\mathcal{M}} f(x) + \\mu \\|x\\|_1$, where $\\mathcal{M}$ is a compact embedded submanifold and $f(x)$ is smooth. Although this method converges superlinearly locally, global convergence is not guaranteed. The existing remedy relies on a hybrid approach: running a Riemannian proximal gradient method until the iterate is sufficiently accurate and switching to the Riemannian proximal Newton method. This existing approach is sensitive to the switching parameter. This paper proposes a Rie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08365","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/2405.08365/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"}