ADAPTIVE GAUSS–NEWTON METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS
In this article, we propose a new version of Gauss–Newton method for solving systems of nonlinear equations based on ideas of the residual upper bound for a system of nonlinear equations and a quadratic regularization term. We prove a global convergence for the presented method. Under natural assumptions we establish a global linear convergence. The proposed method uses an adaptive strategy to choose hyperparameters of a local model forming a flexible and convenient method, implementable using standard convex optimization techniques.