  We study iterative regularization for linear models, when the bias is convex
but not necessarily strongly convex. We characterize the stability properties
of a primal-dual gradient based approach, analyzing its convergence in the
presence of worst case deterministic noise. As a main example, we specialize
and illustrate the results for the problem of robust sparse recovery. Key to
our analysis is a combination of ideas from regularization theory and
optimization in the presence of errors. Theoretical results are complemented by
experiments showing that state-of-the-art performances can be achieved with
considerable computational speed-ups.
