Irregular operator equations by iterative methods with undetermined reverse connection

In this paper, the possibility of using the reverse connection control for iteratively regularized Gauss–Newton-type algorithms is analyzed. It is shown that for the generalized Gauss–Newton iterations the diameter of the set containing the control elements can tend to ∞ as n → ∞. To further improve the stabilizing properties of the Gauss–Newton scheme, a new penalty term is proposed that can depend nonlinearly on the current iteration. As a test numerical example, a nonlinear inverse scattering problem of computing a 2D obstacle shape is considered.