Convergence properties of Levenberg–Marquardt methods with generalized regularization terms

Shumpei Ariizumi, Yuya Yamakawa and Nobuo Yamashita

Applied Mathematics and Computation, 2024, vol. 463, issue C

Abstract: Levenberg–Marquardt methods (LMMs) are the most typical algorithms for solving nonlinear equations F(x)=0, where F:Rn→Rm is a continuously differentiable function. They sequentially solve subproblems represented as squared residual of the Newton equations with the L2 regularization to determine the search direction. However, since the subproblems of the LMMs are usually reduced to linear equations with n variables, it takes much time to solve them when m≪n.

Keywords: Nonlinear equation; Levenberg–Marquardt method; Global convergence; Local convergence (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005349

DOI: 10.1016/j.amc.2023.128365

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