{"paper":{"title":"On the Universality of Simple Trust-Region Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Clemens Sirotenko","submitted_at":"2026-07-22T01:06:15Z","abstract_excerpt":"We establish universal complexity guarantees for quadratic trust-region methods and identify a common mechanism underlying their universal behavior under convexity, based on a function-gap model-decrease estimate that appears to be new in the trust-region literature. First, we prove that the basic trust-region method with inexact subproblem solves is universal under convexity. Under a $\\nu$-H\\\"older-continuous Hessian, it attains the global complexity bound $\\mathcal{O}(\\varepsilon^{-1/(1+\\nu)})$ for computing an $\\varepsilon$-approximate minimizer, without knowledge of $\\nu\\in[0,1]$ or the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19647","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/2607.19647/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"}