  This paper aims to investigate the effectiveness of the recently proposed
Boosted Difference of Convex functions Algorithm (BDCA) when applied to
clustering with constraints and set clustering with constraints problems. This
is the first paper to apply BDCA to a problem with nonlinear constraints. We
present the mathematical basis for the BDCA and Difference of Convex functions
Algorithm (DCA), along with a penalty method based on distance functions. We
then develop algorithms for solving these problems and computationally
implement them, with publicly available implementations. We compare old
examples and provide new experiments to test the algorithms. We find that the
BDCA method converges in fewer iterations than the corresponding DCA-based
method. In addition, BDCA yields faster CPU running-times in all tested
problems.
