A convergence analysis of the iteratively regularized Gauss-Newton method under Lipschitz condition

TL;DR

This paper analyzes the convergence of the iteratively regularized Gauss-Newton method for nonlinear ill-posed inverse problems under Lipschitz conditions, demonstrating its optimal regularization properties with an appropriate stopping rule.

Contribution

It provides a convergence analysis under Lipschitz conditions and establishes the optimality of the method with an a posteriori stopping rule.

Findings

Method converges under Lipschitz condition

Achieves order optimal regularization

Suitable stopping rule ensures optimality

Abstract

In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.