The reconstruction of artifact-free images from radially encoded MRI acquisitions poses a difficult task for undersampled data sets, that is for a much lower number of spokes in k-space than data samples per spoke. Here, we developed an iterative reconstruction method for undersampled radial MRI which (i) is based on a nonlinear optimization, (ii) allows for the incorporation of prior knowledge with use of penalty functions, and (iii) deals with data from multiple coils. The procedure arises as a two-step mechanism which first estimates the coil profiles and then renders a final image that complies with the actual observations. Prior knowledge is introduced by penalizing edges in coil profiles and by a total variation constraint for the final image. The latter condition leads to an effective suppression of undersampling (streaking) artifacts and further adds a certain degree of denoising. Apart from simulations, experimental results for a radial spin-echo MRI sequence are presented for phantoms and human brain in vivo at 2.9 T using 24, 48, and 96 spokes with 256 data samples. In comparison to conventional reconstructions (regridding) the proposed method yielded visually improved image quality in all cases.