On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation

TL;DR

This paper introduces a trust-region method with adaptive regularization for solving nonlinear ill-posed systems, demonstrating both theoretical regularization properties and numerical validation to ensure stable solutions.

Contribution

It proposes a novel trust-region approach with adaptive regularization that effectively addresses the ill-posedness of nonlinear systems, with theoretical and numerical support.

Findings

The method can approach solutions of unperturbed systems.

Theoretical proof of regularization properties.

Numerical experiments validate effectiveness.

Abstract

In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a solution of the unperturbed system. This regularizing property is shown theoretically and validated numerically.