DOUBLE-INERTIAL PROXIMAL GRADIENT ALGORITHM FOR DIFFERENCE-OF-CONVEX PROGRAMMING

In this paper we study a class of difference-of-convex programming whose objective function is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a proper closed concave function composited with a linear operator. First, we consider the primal-dual reformulation of difference-of-convex programming. Then, adopting the framework of the double-proximal gradient algorithm (DPGA) and the inertial technique for accelerating the first-order algorithms, we propose a double-inertial proximal gradient algorithm (DiPGA) which includes some classical algorithms as its special cases. Under the assumption that the underlying function satisfies the Kurdyka-Lojasiewicz (KL) property and some suitable conditions on the parameters, we prove that each bounded sequence generated by DiPGA globally converges to a critical point of the objective function. Finally, we apply the algorithm to image processing model and compare it with DPGA to show its efficiency.