  In this paper we consider the iteratively regularized Gauss-Newton method,
where regularization is achieved by Ivanov regularization, i.e., by imposing a
priori constraints on the solution. We propose an a posteriori choice of the
regularization radius, based on an inexact Newton / discrepancy principle
approach, prove convergence and convergence rates under a variational source
condition as the noise level tends to zero, and provide an analysis of the
discretization error. Our results are valid in general, possibly nonreflexive
Banach spaces, including, e.g., $L^\infty$ as a preimage space. The theoretical
findings are illustrated by numerical experiments.
