Adaptive Gauss–Newton Method for Solving Systems of Nonlinear Equations

Doklady Mathematics. 2021. Vol. 104. No. 2. P. 293–296.

Юдин Н. Е.

Переводчик: I. Ruzanova

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.

Ключевые слова: inexact oracle, Complexity estimate, systems of nonlinear equations, unimodal optimization, Gauss–Newton method, Polyak–Łojasiewicz condition, inexact proximal mapping, underdetermined model