  We consider a class of difference-of-convex (DC) optimization problems where
the objective function is the sum of a smooth function and a possible nonsmooth
DC function. The application of proximal DC algorithms to address this problem
class is well-known. In this paper, we combine a proximal DC algorithm with an
inexact proximal Newton-type method to propose an inexact proximal DC
Newton-type method. We demonstrate global convergence properties of the
proposed method. In addition, we give a memoryless quasi-Newton matrix for
scaled proximal mappings and consider a two-dimensional system of semi-smooth
equations that arise in calculating scaled proximal mappings. To efficiently
obtain the scaled proximal mappings, we adopt a semi-smooth Newton method to
inexactly solve the system. Finally, we present some numerical experiments to
investigate the efficiency of the proposed method, showing that the proposed
method outperforms existing methods.
