Convergence analysis of a regularized Newton method with generalized regularization terms for convex optimization problems
Year: 2024
Type: preprint
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 $\mathcal{O}(k^{-2})$ and local superlinear convergence, which are the same as those of the cubic RNM.
Source: arXiv (Cornell University)
Authors: Yamakawa, Yuya, Yamashita, Nobuo
Institution: Kyoto University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4399759083