  We develop a parametric high-resolution method for the estimation of the
frequency nodes of linear combinations of complex exponentials with exponential
damping. We use Kronecker's theorem to formulate the associated nonlinear least
squares problem as an optimization problem in the space of vectors generating
Hankel matrices of fixed rank. Approximate solutions to this problem are
obtained by using the alternating direction method of multipliers. Finally, we
extract the frequency estimates from the con-eigenvectors of the solution
Hankel matrix. The resulting algorithm is simple, easy to implement and can be
applied to data with equally spaced samples with approximation weights, which
for instance allows cases of missing data samples. By means of numerical
simulations, we analyze and illustrate the excellent performance of the method,
attaining the Cram\'er-Rao bound.
