A smoothing moving balls approximation method for a class of conic-constrained difference-of-convex optimization problems

[2505.12314] A smoothing moving balls approximation method for a class of conic-constrained difference-of-convex optimization problems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2505.12314 (math) [Submitted on 18 May 2025 ( v1 ), last revised 20 Jul 2026 (this version, v3)] Title: A smoothing moving balls approximation method for a class of conic-constrained difference-of-convex optimization problems Authors: Jiefeng Xu , Ting Kei Pong , Nung-sing Sze View a PDF of the paper titled A smoothing moving balls approximation method for a class of conic-constrained difference-of-convex optimization problems, by Jiefeng Xu and 2 other authors View PDF HTML (experimental) Abstract: In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact base of the polar cone exhibits a majorizing smoothing approximation, a condition that is satisfied by widely studied cones such as $\mathbb{R}^m_-$ and ${\cal S}^m_-$. Leveraging this condition, we reformulate the conic constraint equivalently as a single constraint involving the aforementioned support function, and adapt the moving balls approximation (MBA) method for its solution. In essence, in each iteration of our algorithm, we approximate the support function by a smooth approximation function and apply one MBA step. The subproblems that arise in our algorithm always involve only one single inequality constraint, and can thus be solved efficiently via one-dimensional root-finding procedures. We design explicit rules to evolve the smooth approximation functions from iteration to iteration and establish the corresponding iteration complexity for obtaining an $(\epsilon_1, \epsilon_2, \epsilon_1 \sqrt{\epsilon_2})$-Karush-Kuhn-Tucker point. In addition, in the convex setting, we establish convergence of the sequence generated, and study its local convergence rate under a standard Hölderian growth condition. Finally, we perform numerical experiments to illustrate the performance of our algorithm. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2505.12314 [math.OC] (or arXiv:2505.12314v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2505.12314 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ting Kei Pong [ view email ] [v1] Sun, 18 May 2025 09:01:03 UTC (381 KB) [v2] Fri, 10 Apr 2026 09:57:21 UTC (371 KB) [v3] Mon, 20 Jul 2026 14:01:47 UTC (371 KB) Full-text links: Access Paper: View a PDF of the paper titled A smoothing moving balls approximation method for a class of conic-constrained difference-of-convex optimization problems, by Jiefeng Xu and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-05 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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