On the global complexity of a derivative-free Levenberg-Marquardt algorithm via orthogonal spherical smoothing

2024/07/17 by Xi Chen, Chen, Xi, Jinyan Fan +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2407.12542

openalex publication_date 2024/07/17 · openalex created_date 2024/09/09 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a derivative-free Levenberg-Marquardt algorithm for nonlinear least squares problems, where the Jacobian matrices are approximated via orthogonal spherical smoothing. It is shown that the gradient models which use the approximate Jacobian matrices are probabilistically first-order accurate, and the high probability complexity bound of the algorithm is also given.

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• A derivative-free Levenberg-Marquardt method for sparse nonlinear least squares problems

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