  In this paper, we present two variants of DCA (Different of Convex functions
Algorithm) to solve the constrained sum of differentiable function and
composite functions minimization problem, with the aim of increasing the
convergence speed of DCA. In the first variant, DCA-Like, we introduce a new
technique to iteratively modify the decomposition of the objective function.
This successive decomposition could lead to a better majorization and
consequently a better convergence speed than the basic DCA. We then incorporate
the Nesterov's acceleration technique into DCA-Like to give rise to the second
variant, named Accelerated DCA-Like. The convergence properties and the
convergence rate under Kudyka-Lojasiewicz assumption of both variants are
rigorously studied. As an application, we investigate our algorithms for the
t-distributed stochastic neighbor embedding. Numerical experiments on several
benchmark datasets illustrate the efficiency of our algorithms.
