On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems

Summary.

In the study of the choice of the regularization parameter for Tikhonov regularization of nonlinear ill-posed problems, Scherzer, Engl and Kunisch proposed an a posteriori strategy in 1993. To prove the optimality of the strategy, they imposed many very restrictive conditions on the problem under consideration. Their results are difficult to apply to concrete problems since one can not make sure whether their assumptions are valid. In this paper we give a further study on this strategy, and show that Tikhonov regularization is order optimal for each $0<\nu\le 2$ with the regularization parameter chosen according to this strategy under some simple and easy-checking assumptions. This paper weakens the conditions needed in the existing results, and provides a theoretical guidance to numerical experiments.