  In this work the minimization problem for the difference of convex (DC)
functions is studied by using Moreau envelopes and the descent method with
Moreau gradient is employed to approximate the numerical solution. The main
regularization idea in this work is inspired by Hiriart-Urruty [14],
Moudafi[17], regularize the components of the DC problem by adapting the
different parameters and strategic matrices flexibly to evaluate the whole DC
problem. It is shown that the inertial gradient method as well as the classic
gradient descent scheme tend towards an approximation stationary point of the
original problem.
