{"paper":{"title":"Minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"E. Simon, Ph. L. Toint, S. Gratton","submitted_at":"2019-02-27T09:19:09Z","abstract_excerpt":"An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most $O(|\\log(\\epsilon)|\\,\\epsilon^{-2})$ evaluations of the problem's functions and their derivatives for finding an $\\epsilon$-approximate first-order stationary point. This complexity bound therefore generalizes that provided by [Bellavia, Gurioli, Morini and Toint, 2018] for inexact methods for smooth nonconvex problems, and is within a factor $|\\log(\\epsilon)|$ of the optimal bound known"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10406","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":""},"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"}