{"paper":{"title":"ItsOPT: An inexact two-level smoothing framework for nonconvex optimization via high-order Moreau envelope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alireza Kabgani, Masoud Ahookhosh","submitted_at":"2024-10-25T18:54:35Z","abstract_excerpt":"This paper introduces ItsOPT, an {\\it inexact two-level smoothing optimization framework} designed to find first-order critical points of nonsmooth and nonconvex functions. The framework consists of two levels of methodologies: at the upper level, a zeroth-, first-, or second-order method can be tailored to minimize a smooth approximation; at the lower level, the high-order proximal auxiliary problems are solved inexactly, generating an inexact oracle for the smooth function. As a smoothing technique, we introduce the high-order Moreau envelope (HOME) and study its fundamental properties under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19928","kind":"arxiv","version":5},"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/2410.19928/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"}