  In this paper, we focus on the problem of minimizing the sum of a nonconvex
differentiable function and a DC (Difference of Convex functions) function,
where the differentiable function is not restricted to the global Lipschitz
gradient continuity assumption. This problem covers a broad range of
applications in machine learning and statistics such as compressed sensing,
signal recovery, sparse dictionary learning, and matrix factorization, etc. We
take inspiration from the Nesterov's acceleration technique and the DC
algorithm to develop a novel algorithm for the considered problem. Analyzing
the convergence, we study the subsequential convergence of our algorithm to a
critical point. Furthermore, we justify the global convergence of the whole
sequence generated by our algorithm to a critical point and establish its
convergence rate under the Kurdyka-Lojasiewicz condition. Numerical experiments
on the nonnegative matrix completion problem are performed to demonstrate the
efficiency of our algorithm and its superiority over well-known methods.
