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Our analysis reveals that a class of linesearch-free methods is still convergent under mere local H\\\"older gradient continuity, covering in particular continuously differentiable semi-algebraic functions. To mitigate the lack of local Lipschitz continuity, popular approaches revolve around $\\varepsilon$-oracles and/or linesearch procedures. In contrast, we exploit plain H\\\"older inequalities not entailing any approximation, all while retaining the linesearch-free nature of adaptive schemes. Furthermore, we prove full sequence convergence without prior knowledge of local H\\\"older constants nor of the order of H\\\"older continuity. Numerical experiments make comparisons with baseline methods on diverse tasks from machine learning covering both the locally and the globally H\\\"older setting.","url_abs":"https://arxiv.org/abs/2402.06271v2","url_pdf":"https://arxiv.org/pdf/2402.06271v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"adaptive-proximal-gradient-methods-are","repo_url":"https://github.com/emanuellaude/universal-adaptive-proximal-gradient","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.06271","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.06271"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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