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

2024/06/14 by Yuya Yamakawa, Yamakawa, Yuya, Nobuo Yamashita +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2406.09786

openalex publication_date 2024/06/14 · openalex created_date 2024/06/18 · openalex updated_date 2026/07/28

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.

Related

• Gradient Regularization of Newton Method with Bregman Distances
• Regularized Newton Method with Global O(1/k²) Convergence
• Cubic Regularization is the Key! The First Accelerated Quasi-Newton Method with a Global Convergence Rate of O(k^-2) for Convex Functions
• Complexity of the Regularized Newton Method
• Super-Universal Regularized Newton Method