  We proposed an iterate scheme for solving convex-concave saddle-point
problems associated with general convex-concave functions. We demonstrated that
when our iterate scheme is applied to a special class of convex-concave
functions, which are constructed by a bilinear coupling term plus a difference
of two convex functions, it becomes a generalization of several popular
primal-dual algorithms from constant involved parameters to involved parameters
as general sequences. For this specific class of convex-concave functions, we
proved that the sequence of function values, taken over the averages of
iterates generated by our scheme, converges to the value of the function at a
saddle-point. Additionally, we provided convergence results for both the
sequence of averages of our iterates and the sequence of our iterates.
  In our numerical experiments, we implemented our algorithm in a matrix game,
a linear program in inequality form, and a least-squares problem with
$\ell_{1}$ regularization. In these examples, we also compared our algorithm
with other primal-dual algorithms where parameters in their iterate schemes
were kept constant. Our experimental results not only validated our theoretical
findings but also demonstrated that our algorithm consistently outperforms
various iterate schemes with constant involved parameters.
