{"paper":{"title":"Difference-of-Convex Optimization via Inexact Smoothing Descent Methods: Difference of High-Order Moreau Envelopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alireza Kabgani, Masoud Ahookhosh, Moslem Zamani","submitted_at":"2026-06-30T00:05:35Z","abstract_excerpt":"This paper studies difference-of-convex (DC) optimization problems through smoothing descent techniques. In particular, we introduce the difference of high-order Moreau envelopes (HOME-DC) and establish its fundamental and differential properties. Approximating the underlying proximal points, we generate an inexact first-order oracle for HOME-DC and characterize its accuracy guarantees. Building upon this oracle, we propose a class of inexact descent methods for minimizing DC functions and provide a convergence analysis. The proposed framework extends the applicability of envelope-based optimi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30991","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/2606.30991/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"}