  The Difference of Convex functions Algorithm (DCA) is widely used for
minimizing the difference of two convex functions. A recently proposed
accelerated version, termed BDCA for Boosted DC Algorithm, incorporates a line
search step to achieve a larger decrease of the objective value at each
iteration. Thanks to this step, BDCA usually converges much faster than DCA in
practice. The solutions found by DCA are guaranteed to be critical points of
the problem, but these may not be local minima. Although BDCA tends to improve
the objective value of the solutions it finds, these are frequently just
critical points as well. In this paper we combine BDCA with a simple
Derivative-Free Optimization (DFO) algorithm to force the d-stationarity (lack
of descent direction) at the point obtained. The potential of this approach is
illustrated through some computational experiments on a Minimum-Sum-of-Squares
clustering problem. Our numerical results demonstrate that the new method
provides better solutions while still remains faster than DCA in the majority
of test cases.
