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Convergence analysis of a regularized Newton method with generalized regularization terms for unconstrained convex optimization problems

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  • Yamakawa, Yuya
  • Yamashita, Nobuo

Abstract

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special cases. Therefore, the proposed method serves as a general framework that includes not only the classical and cubic RNMs but also a novel RNM with elastic net regularization. We show that the proposed RNM has the global O(k−2) and local superlinear convergence, which are the same as those of the cubic RNM.

Suggested Citation

  • Yamakawa, Yuya & Yamashita, Nobuo, 2025. "Convergence analysis of a regularized Newton method with generalized regularization terms for unconstrained convex optimization problems," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    • Handle: RePEc:eee:apmaco:v:491:y:2025:i:c:s0096300324006805
    DOI: 10.1016/j.amc.2024.129219
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    References listed on IDEAS

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    1. Ariizumi, Shumpei & Yamakawa, Yuya & Yamashita, Nobuo, 2024. "Convergence properties of Levenberg–Marquardt methods with generalized regularization terms," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    2. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Ying-Jie Li & Dong-Hui Li, 2009. "Truncated regularized Newton method for convex minimizations," Computational Optimization and Applications, Springer, vol. 43(1), pages 119-131, May.
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    Cited by:

    1. Jianyu Xiao & Haibin Zhang & Huan Gao, 2025. "A Chebyshev–Halley Method with Gradient Regularization and an Improved Convergence Rate," Mathematics, MDPI, vol. 13(8), pages 1-17, April.

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