Levenberg–Marquardt method based on probabilistic Jacobian models for nonlinear equations

Ruixue Zhao () and Jinyan Fan ()
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Ruixue Zhao: Shanghai University of Finance and Economics
Jinyan Fan: Shanghai Jiao Tong University

Computational Optimization and Applications, 2022, vol. 83, issue 2, No 1, 401 pages

Abstract: Abstract In this paper, we propose a Levenberg–Marquardt method based on probabilistic models for nonlinear equations for which the Jacobian cannot be computed accurately or the computation is very expensive. We introduce the definition of the first-order accurate probabilistic Jacobian model, and show how to construct such a model with sample points generated by standard Gaussian distribution. Under certain conditions, we prove that the proposed method converges to a first order stationary point with probability one. Numerical results show the efficiency of the method.

Keywords: Levenberg–Marquardt method; Probabilistic Jacobian models; Derivative-free optimization; Global convergence; 65K10; 15A18; 65F15; 90C22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00393-9

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