  We revisit the classical dual ascent algorithm for minimization of convex
functionals in the presence of linear constraints, and give convergence results
which apply even for non-convex functionals. We describe limit points in terms
of the convex envelope. We also introduce a new augmented version, which is
shown to have superior convergence properties, and provide new results even for
convex but non-differentiable objective functionals (as well as non-convex).
  The results are applied to low rank approximation of a given matrix, subject
to linear constraints. In particular, letting the linear constraints enforce
Hankel structure of the respective matrices, the algorithms can be applied to
complex frequency estimation. We provide numerical tests in this setting.
