Sequential-data-driven Levenberg-Marquardt algorithm with convex constraints

Wei Wang

doi:10.1016/j.jco.2026.102027

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Sequential-data-driven Levenberg-Marquardt algorithm with convex constraints

2026-02-01

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Wei Wang

Min Zhong *

Kai Zhu

DOI：10.1016/j.jco.2026.102027

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Abstract

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Extracting useful information and assimilating new data are crucial in many parameter identification and state estimation problems. The full utilization of newly generated data can lead to rapid reconstructions. However, most existing regularization methods for solving such inverse problems typically rely on a single observed dataset. In this manuscript, we introduce the statistical nonlinear regularization method called the Iterated Levenberg-Marquardt-O (IRLM-O) method. This method builds upon the Levenberg-Marquardt algorithm and is specifically designed to handle sequential data and random noise. The method incorporates a general convex functional O, which is selected based on the regularity information of the sought solution. Penalty terms such as L1 or TV-like terms can be included, which are essential to reconstruct solutions with sparsity or discontinuities. We consider three types of observations, leading to three methods: averaged (aIRLM-O), dynamical (dIRLM-O) and naive (nIRLM-O), respectively. Under reasonable assumptions, the theoretical foundations for these methods are developed, including a preliminary error estimate and convergence analysis. Some strategies apriori for stopping criteria are also discussed. Finally, we present two parameter identification problems to demonstrate the efficiency and practicality of the proposed methods. (c) 2026 Published by Elsevier Inc.

Keywords:

Inverse problems

Iterative regularization

Levenberg-Marquardt method

Convex penalty term

Sequential data