  In this paper, we study the convergence rate of the DCA (Difference-of-Convex
Algorithm), also known as the convex-concave procedure, with two different
termination criteria that are suitable for smooth and nonsmooth decompositions
respectively. The DCA is a popular algorithm for difference-of-convex (DC)
problems, and known to converge to a stationary point of the objective under
some assumptions. We derive a worst-case convergence rate of $O(1/\sqrt{N})$
after $N$ iterations of the objective gradient norm for certain classes of DC
problems, without assuming strong convexity in the DC decomposition, and give
an example which shows the convergence rate is exact. We also provide a new
convergence rate of $O(1/N)$ for the DCA with the second termination criterion.
%In addition, we investigate the DCA with regularization. Moreover, we derive a
new linear convergence rate result for the DCA under the assumption of the
Polyak-\L ojasiewicz inequality. The novel aspect of our analysis is that it
employs semidefinite programming performance estimation.
