  In this paper, we consider a class of difference-of-convex (DC) optimization
problems, where the global Lipschitz gradient continuity assumption on the
smooth part of the objective function is not required. Such problems are
prevalent in many contemporary applications such as compressed sensing,
statistical regression, and machine learning, and can be solved by a general
Bregman proximal DC algorithm (BPDCA). However, the existing BPDCA is developed
based on the stringent requirement that the involved subproblems must be solved
exactly, which is often impractical and limits the applicability of the BPDCA.
To facilitate the practical implementations and wider applications of the
BPDCA, we develop an inexact Bregman proximal difference-of-convex algorithm
(iBPDCA) by incorporating two types of relative-type stopping criteria for
solving the subproblems. The proposed inexact framework has considerable
flexibility to encompass many existing exact and inexact methods, and can
accommodate different types of errors that may occur when solving the
subproblem. This enables the potential application of our inexact framework
across different DC decompositions to facilitate the design of a more efficient
DCA scheme in practice. The global subsequential convergence and the global
sequential convergence of our iBPDCA are established under suitable conditions
including the Kurdyka-{\L}ojasiewicz property. Some numerical experiments on
the $\ell_{1-2}$ regularized least squares problem and the constrained
$\ell_{1-2}$ sparse optimization problem are conducted to show the superior
performance of our iBPDCA in comparison to existing algorithms. These results
also empirically verify the necessity of developing different types of stopping
criteria to facilitate the efficient computation of the subproblem in each
iteration of our iBPDCA.
