An Inertial Bregman Proximal DC Algorithm for Generalized DC Programming with Application to Data Completion

Abstract: In this paper, we consider a class of generalized difference-of-convex functions (DC) programming, whose objective is the difference of two convex (not necessarily smooth) functions plus a decomposable (possibly nonconvex) function with Lipschitz gradient. By employing the Fenchel-Young inequality and Moreau decomposition theorem, we introduce an inertial Bregman proximal DC algorithm to solve the problem under consideration. Our algorithmic framework is able to fully exploit the decomposable structure of the generalized DC programming such that each subproblem of the algorithm is enough easy in many cases. Theoretically, we show that the sequence generated by the proposed algorithm globally converges to a critical point under the Kurdyka-{\L}ojasiewicz condition. A series of numerical results demonstrate that our algorithm runs efficiently on matrix and tensor completion problems.