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

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 f...

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Bibliographic Details
Published in:Applied mathematics and computation 2025-04, Vol.491, Article 129219
Main Authors: Yamakawa, Yuya, Yamashita, Nobuo
Format: Article
Language:English
Subjects:
Generalized regularization
Global [formula omitted] convergence
Local convergence
Regularized Newton method
Superlinear convergence
Unconstrained convex optimization
Online Access:Get full text
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Summary: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.
ISSN:0096-3003
DOI:10.1016/j.amc.2024.129219