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. 
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/
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     title = {Adaptive {Gauss{\textendash}Newton} method for solving systems of nonlinear equations},
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