Iterative regularization for constrained minimization formulations of nonlinear inverse problems

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss applicability to the problem of identifying the spatially varying diffusivity in an elliptic PDE from different sets of observations. Among these is a novel hybrid imaging techology known as impedance acoustic tomography, for which we provide numerical experiments.