A split Levenberg-Marquardt method for large-scale sparse problems

Nataša Krejić (), Greta Malaspina () and Lense Swaenen ()
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Nataša Krejić: University of Novi Sad
Greta Malaspina: University of Novi Sad
Lense Swaenen: Mathware department, Sioux Technologies

Computational Optimization and Applications, 2023, vol. 85, issue 1, No 5, 147-179

Abstract: Abstract We consider large-scale nonlinear least squares problems with sparse residuals, each of them depending on a small number of variables. A decoupling procedure which results in a splitting of the original problems into a sequence of independent problems of smaller sizes is proposed and analysed. The smaller size problems are modified in a way that offsets the error made by disregarding dependencies that allow us to split the original problem. The resulting method is a modification of the Levenberg-Marquardt method with smaller computational costs. Global convergence is proved as well as local linear convergence under suitable assumptions on sparsity. The method is tested on the network localization simulated problems with up to one million variables and its efficiency is demonstrated.

Keywords: Least squares problems; Levenberg Marquardt method; Splitting; Local linear convergence; Global convergence (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00460-9

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