  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.
