Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems

Abstract

Trust region methods have been well developed for well-posed problems, but there is little literature available on their applications to ill-posed inverse problems. In this paper, we apply trust region methods for solving nonlinear ill-posed inverse problems. In particular, we study the convergence and regularity of the standard trust region method when applying it to ill-posed problems. We also show that the trust region method is a regularization. A numerical test on inverse gravimetry is included to demonstrate our theoretical analysis and regularization property of the trust region method.