Adaptive Gauss–Newton Method for Solving Systems
of Nonlinear Equations
N. E. Yudina,b,*
a Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
b Federal Research Center “Informatics and Control,” Russian Academy of Sciences, Moscow, Russia
Correspondence to: *e-mail: iudin.ne@phystech.edu
Received 27 May, 2021
Abstract—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
DOI: 10.1134/S1064562421050161