Geodesic
Adaptive Gauss--Newton method for solving systems of nonlinear equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 87-91

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For systems of nonlinear equations, we propose a new version of the Gauss–Newton method based on the idea of using an upper bound for the residual norm of the system and a quadratic regularization term. The global convergence of the method is proved. Under natural assumptions, global linear convergence is established. The method uses an adaptive strategy to choose hyperparameters of a local model, thus forming a flexible and convenient algorithm that can be implemented using standard convex optimization techniques.
Keywords: systems of nonlinear equations, unimodal optimization, Gauss–Newton method, Polyak–Łojasiewicz condition, inexact proximal mapping inexact oracle, underdetermined model, complexity estimate. 
@article{DANMA_2021_500_a15,
     author = {N. E. Yudin},
     title = {Adaptive {Gauss--Newton} method for solving systems of nonlinear equations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {87--91},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a15/}
}
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N. E. Yudin. Adaptive Gauss--Newton method for solving systems of nonlinear equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 87-91. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a15/