{"paper":{"title":"Optimal Deterministic Oracle Complexity for Weakly Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiajin Li, Siyu Pan","submitted_at":"2026-08-04T07:15:54Z","abstract_excerpt":"We study the oracle complexity of finding $\\epsilon$-stationary points of $\\rho$-weakly convex and $G$-Lipschitz functions, where stationarity is measured by the gradient of the Moreau envelope. We consider a first-order oracle that returns both the function value and the full subdifferential at every query point. We prove that every deterministic first-order algorithm requires $ \\Omega({\\rho G^2\\Delta}/{\\epsilon^4})$ oracle queries whenever $\\Delta \\leq {G^2}/{\\rho}$, where $f(\\bz)-\\inf f \\leq \\Delta$. This lower bound matches the best known deterministic and stochastic first-order upper boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03246","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/2608.03246/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"}