Work

An Enhanced Levenberg--Marquardt Method via Gram Reduction

Year: 2025

Type: conference-paper

Abstract: This paper studies the problem of solving the system of nonlinear equations. We propose the Gram-reduced Levenberg--Marquardt method, which reuses the Gram matrix. Our method has a global convergence guarantee without relying on any step of line-search or solving sub-problems. We show that our method takes a smaller computational complexity than existing Levenberg--Marquardt methods to find the stationary point of the square norm of the equations. We also show that the proposed method enjoys a local superlinear convergence rate under the non-degenerate assumption. Experiments are conducted on real-world applications in scientific computing and machine learning, which validate the efficiency of our method.

Source: Proceedings of the AAAI Conference on Artificial Intelligence

DOI: 10.1609/aaai.v39i18.34066

Authors: Chengchang Liu, Luo Luo, John C.S. Lui

Institutions: Chinese University of Hong Kong, Fudan University

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G881682259