{"paper":{"title":"Convergence of the Safeguarded Augmented Lagrangian Method under the Polyak-Lojasiewicz constraint qualification for Constrained Composite Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christian Kanzow, Jannis Kr\\\"uger","submitted_at":"2026-06-24T08:44:22Z","abstract_excerpt":"In this work we provide theoretical and practical results of the Safeguarded Augmented Lagrangian Method (SALM) for constrained composite optimization problems whose objective is the sum of a smooth and a nonsmooth function. We obtain global convergence results to an M-stationary point for SALM under the Polyak-Lojasiewicz constraint qualification (PLCQ). For this result the boundedness of the Lagrange multipliers is crucial, and this is shown under the assumption that the nonsmooth part of the objective function is locally Lipschitz continuous. A counterexample shows that one cannot expect to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25567","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25567/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"}