{"paper":{"title":"A Finite-Difference Trust-Region Method for Convexly Constrained Smooth Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"D\\^an\\^a Davar, Geovani Nunes Grapiglia","submitted_at":"2025-10-20T10:05:21Z","abstract_excerpt":"We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. For nonconvex problems, we establish a worst-case complexity bound of $\\mathcal{O}\\!\\left(n\\left(\\frac{L}{\\sigma}\\epsilon\\right)^{-2}\\right)$ function evaluations for the method to reach an $\\left(\\frac{L}{\\sigma}\\epsilon\\right)$-approximate stationary point, where $n$ is the number of variables, $L$ is the Lipschitz constant of the gradient, and $\\sigma$ is a user-defined estimate of $L$. If the objective function is convex, the complexi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.17366","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/2510.17366/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"}