{"paper":{"title":"Convergence rates of regularized quasi-Newton methods without strong convexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jalal Fadili, Peter Ochs, Shida Wang","submitted_at":"2025-05-31T11:48:12Z","abstract_excerpt":"In this paper, we study convergence rates of the cubic regularized proximal quasi-Newton method (\\csr) for solving non-smooth additive composite problems that satisfy the so-called Kurdyka-\\L ojasiewicz (K\\L ) property with respect to some desingularization function $\\phi$ rather than strong convexity. After a number of iterations $k_0$, Cubic SR1 PQN exhibits non-asymptotic explicit super-linear convergence rates for any $k\\geq k_0$. In particular, when $\\phi(t)=ct^{1/2}$, Cubic SR1 PQN has a convergence rate of order $\\left(\\frac{C}{(k-k_0)^{1/2}}\\right)^{(k-k_0)/2}$, where $k$ is the number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00521","kind":"arxiv","version":6},"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/2506.00521/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"}