{"paper":{"title":"Universal and Parameter-free Gradient Sliding for Composite Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Qi Luo, Yan Wu, Yuyuan Ouyang, Zhe Zhang","submitted_at":"2026-03-24T17:57:36Z","abstract_excerpt":"We propose a Parameter-Free Universal Gradient Sliding (PFUGS) algorithm for computing an approximate solution to the convex composite optimization $\\min_{x\\in X} \\{f(x) + g(x)\\}$, where $f$ has $(M_\\nu,\\nu)$-H\\\"older continuous subgradient and $g$ has $L$-Lipschitz continuous gradient. PFUGS computes an $\\varepsilon$-approximate solution with $\\mathcal{O}((M_\\nu/\\varepsilon)^{{2}/{(1+3\\nu)}})$ evaluations of (sub)gradients of $f$ and $\\mathcal{O}((L/\\varepsilon)^{1/2})$ evaluations of gradients of $g$, without prior knowledge of problem constants. To the best of our knowledge, PFUGS is the fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.23492","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/2603.23492/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"}