{"paper":{"title":"Oracle complexities of augmented Lagrangian methods for nonsmooth manifold optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiang Hu, Jiayuan Wu, Kangkang Deng, Zaiwen Wen","submitted_at":"2024-04-08T00:46:59Z","abstract_excerpt":"In this paper, we present two novel manifold inexact augmented Lagrangian methods, \\textbf{ManIAL} for deterministic settings and \\textbf{StoManIAL} for stochastic settings, solving nonsmooth manifold optimization problems. By using the Riemannian gradient method as a subroutine, we establish an $\\mathcal{O}(\\epsilon^{-3})$ oracle complexity result of \\textbf{ManIAL}, matching the best-known complexity result. Our algorithm relies on the careful selection of penalty parameters and the precise control of termination criteria for subproblems. Moreover, for cases where the smooth term follows an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.05121","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/2404.05121/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"}