{"ID":5439554,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-02T23:45:32.241992796Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.30991","arxiv_id":"2606.30991","title":"Difference-of-Convex Optimization via Inexact Smoothing Descent Methods: Difference of High-Order Moreau Envelopes","abstract":"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 optimization techniques to a broad class of structured nonconvex problems while accommodating inexact solutions to subproblems. Preliminary numerical experiments on a sparse clustering problem demonstrate the approach's practical potential and support the theoretical findings.","short_abstract":"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 fir...","url_abs":"https://arxiv.org/abs/2606.30991","url_pdf":"https://arxiv.org/pdf/2606.30991v1","authors":"[\"Alireza Kabgani\",\"Moslem Zamani\",\"Masoud Ahookhosh\"]","published":"2026-06-30T00:05:35Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}