In this paper, we propose a clean and general proof framework to establish
the convergence analysis of the Difference-of-Convex (DC) programming algorithm
(DCA) for both standard DC program and convex constrained DC program. We first
discuss suitable assumptions for the well-definiteness of DCA. Then, we focus
on the convergence analysis of DCA, in particular, the global convergence of
the sequence {xk} generated by DCA under the Lojasiewicz subgradient
inequality and the Kurdyka-Lojasiewicz property respectively. Moreover, the
convergence rate for the sequences {f(xk)} and {β₯xkβxββ₯} are also
investigated. We hope that the proof framework presented in this article will
be a useful tool to conveniently establish the convergence analysis for many
variants of DCA and new DCA-type algorithms