Convergence of a stochastic variance reduced Levenberg–Marquardt method

Weiyi Shao () and Jinyan Fan ()
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Weiyi Shao: Shanghai Jiao Tong University
Jinyan Fan: Shanghai Jiao Tong University

Computational Optimization and Applications, 2025, vol. 90, issue 2, No 4, 417-444

Abstract: Abstract In this paper, we study the empirical residual optimization problem with a least squares loss function. A stochastic variance reduced Levenberg–Marquardt method is proposed for solving it. It is shown that both the estimates and the models of the objective function are probabilistically weak accurate if the sample size is chosen appropriately. Moreover, the method converges to a stationary point of the problem almost surely under certain conditions.

Keywords: Least squares problems; Empirical residual optimization problem; Stochastic Levenberg–Marquardt algorithm; Variance reduced method; Mini-batch estimation; 65K05; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00639-8

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